Question
Solve the equation
Solve for x
x1=−17,x2=−15,x3=15,x4=17
Alternative Form
x1≈−4.123106,x2≈−3.872983,x3≈3.872983,x4≈4.123106
Evaluate
5x−20(x+41)−(x−41)÷(x2−16)=−5(x−4)8
Find the domain
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Evaluate
⎩⎨⎧x+4=0x−4=05x−20=0x2−16=05(x−4)=0
Calculate
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Evaluate
x+4=0
Move the constant to the right side
x=0−4
Removing 0 doesn't change the value,so remove it from the expression
x=−4
⎩⎨⎧x=−4x−4=05x−20=0x2−16=05(x−4)=0
Calculate
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Evaluate
x−4=0
Move the constant to the right side
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
⎩⎨⎧x=−4x=45x−20=0x2−16=05(x−4)=0
Calculate
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Evaluate
5x−20=0
Move the constant to the right side
5x=0+20
Removing 0 doesn't change the value,so remove it from the expression
5x=20
Divide both sides
55x=520
Divide the numbers
x=520
Divide the numbers
x=4
⎩⎨⎧x=−4x=4x=4x2−16=05(x−4)=0
Calculate
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Evaluate
x2−16=0
Move the constant to the right side
x2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±16
Simplify the expression
x=±4
Separate the inequality into 2 possible cases
{x=4x=−4
Find the intersection
x∈(−∞,−4)∪(−4,4)∪(4,+∞)
⎩⎨⎧x=−4x=4x=4x∈(−∞,−4)∪(−4,4)∪(4,+∞)5(x−4)=0
Calculate
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Evaluate
5(x−4)=0
Rewrite the expression
x−4=0
Move the constant to the right side
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
⎩⎨⎧x=−4x=4x=4x∈(−∞,−4)∪(−4,4)∪(4,+∞)x=4
Simplify
⎩⎨⎧x=−4x=4x∈(−∞,−4)∪(−4,4)∪(4,+∞)
Find the intersection
x∈(−∞,−4)∪(−4,4)∪(4,+∞)
5x−20(x+41)−(x−41)÷(x2−16)=−5(x−4)8,x∈(−∞,−4)∪(−4,4)∪(4,+∞)
Simplify
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Evaluate
5x−20(x+41)−(x−41)÷(x2−16)
Remove the unnecessary parentheses
5x−20x+41−(x−41)÷(x2−16)
Remove the unnecessary parentheses
5x−20x+41−x−41÷(x2−16)
Divide the terms
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Evaluate
5x−20x+41−x−41
Rewrite the expression
5x−20−(x+4)(x−4)8
Multiply by the reciprocal
−(x+4)(x−4)8×5x−201
Multiply the terms
−(x+4)(x−4)(5x−20)8
(−(x+4)(x−4)(5x−20)8)÷(x2−16)
Multiply by the reciprocal
−(x+4)(x−4)(5x−20)8×x2−161
Multiply the terms
−(x+4)(x−4)(5x−20)(x2−16)8
−(x+4)(x−4)(5x−20)(x2−16)8=−5(x−4)8
Rewrite the expression
(x+4)(x−4)(5x−20)(x2−16)−8=5(x−4)−8
Cross multiply
−8×5(x−4)=(x+4)(x−4)(5x−20)(x2−16)(−8)
Simplify the equation
−40(x−4)=(x+4)(x−4)(5x−20)(x2−16)(−8)
Simplify the equation
−40(x−4)=8(−x−4)(x−4)(5x−20)(x2−16)
Rewrite the expression
40(−x+4)=40(−x−4)(x−4)2(x2−16)
Evaluate
−x+4=(−x−4)(x−4)2(x2−16)
Expand the expression
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Evaluate
(−x−4)(x−4)2(x2−16)
Expand the expression
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Evaluate
(x−4)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×4+42
Calculate
x2−8x+16
(−x−4)(x2−8x+16)(x2−16)
Multiply the terms
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Evaluate
(−x−4)(x2−8x+16)
Apply the distributive property
−x×x2−(−x×8x)−x×16−4x2−(−4×8x)−4×16
Multiply the terms
−x3−(−x×8x)−x×16−4x2−(−4×8x)−4×16
Multiply the terms
−x3−(−8x2)−x×16−4x2−(−4×8x)−4×16
Use the commutative property to reorder the terms
−x3−(−8x2)−16x−4x2−(−4×8x)−4×16
Multiply the numbers
−x3−(−8x2)−16x−4x2−(−32x)−4×16
Multiply the numbers
−x3−(−8x2)−16x−4x2−(−32x)−64
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x3+8x2−16x−4x2+32x−64
Subtract the terms
−x3+4x2−16x+32x−64
Add the terms
−x3+4x2+16x−64
(−x3+4x2+16x−64)(x2−16)
Apply the distributive property
−x3×x2−(−x3×16)+4x2×x2−4x2×16+16x×x2−16x×16−64x2−(−64×16)
Multiply the terms
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Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
−x5−(−x3×16)+4x2×x2−4x2×16+16x×x2−16x×16−64x2−(−64×16)
Use the commutative property to reorder the terms
−x5−(−16x3)+4x2×x2−4x2×16+16x×x2−16x×16−64x2−(−64×16)
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
−x5−(−16x3)+4x4−4x2×16+16x×x2−16x×16−64x2−(−64×16)
Multiply the numbers
−x5−(−16x3)+4x4−64x2+16x×x2−16x×16−64x2−(−64×16)
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
−x5−(−16x3)+4x4−64x2+16x3−16x×16−64x2−(−64×16)
Multiply the numbers
−x5−(−16x3)+4x4−64x2+16x3−256x−64x2−(−64×16)
Multiply the numbers
−x5−(−16x3)+4x4−64x2+16x3−256x−64x2−(−1024)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x5+16x3+4x4−64x2+16x3−256x−64x2+1024
Add the terms
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Evaluate
16x3+16x3
Collect like terms by calculating the sum or difference of their coefficients
(16+16)x3
Add the numbers
32x3
−x5+32x3+4x4−64x2−256x−64x2+1024
Subtract the terms
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Evaluate
−64x2−64x2
Collect like terms by calculating the sum or difference of their coefficients
(−64−64)x2
Subtract the numbers
−128x2
−x5+32x3+4x4−128x2−256x+1024
−x+4=−x5+32x3+4x4−128x2−256x+1024
Move the expression to the left side
−x+4−(−x5+32x3+4x4−128x2−256x+1024)=0
Calculate the sum or difference
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Evaluate
−x+4−(−x5+32x3+4x4−128x2−256x+1024)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x+4+x5−32x3−4x4+128x2+256x−1024
Add the terms
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Evaluate
−x+256x
Collect like terms by calculating the sum or difference of their coefficients
(−1+256)x
Add the numbers
255x
255x+4+x5−32x3−4x4+128x2−1024
Subtract the numbers
255x−1020+x5−32x3−4x4+128x2
255x−1020+x5−32x3−4x4+128x2=0
Factor the expression
(−4+x)(17−x2)(15−x2)=0
Separate the equation into 3 possible cases
−4+x=017−x2=015−x2=0
Solve the equation
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Evaluate
−4+x=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
x=417−x2=015−x2=0
Solve the equation
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Evaluate
17−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−17
Removing 0 doesn't change the value,so remove it from the expression
−x2=−17
Change the signs on both sides of the equation
x2=17
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±17
Separate the equation into 2 possible cases
x=17x=−17
x=4x=17x=−1715−x2=0
Solve the equation
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Evaluate
15−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−15
Removing 0 doesn't change the value,so remove it from the expression
−x2=−15
Change the signs on both sides of the equation
x2=15
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±15
Separate the equation into 2 possible cases
x=15x=−15
x=4x=17x=−17x=15x=−15
Check if the solution is in the defined range
x=4x=17x=−17x=15x=−15,x∈(−∞,−4)∪(−4,4)∪(4,+∞)
Find the intersection of the solution and the defined range
x=17x=−17x=15x=−15
Solution
x1=−17,x2=−15,x3=15,x4=17
Alternative Form
x1≈−4.123106,x2≈−3.872983,x3≈3.872983,x4≈4.123106
Show Solution