Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=−12,x2=45−33,x3=0,x4=45−17,x5=45+17,x6=45+33,x7=12
Alternative Form
x1=−12,x2≈−0.186141,x3=0,x4≈0.219224,x5≈2.280776,x6≈2.686141,x7=12
Evaluate
(2x2−5x×1)x2−4∣x∣×3=1
Simplify
More Steps
Evaluate
(2x2−5x×1)x2−4∣x∣×3
Multiply the terms
(2x2−5x)x2−4∣x∣×3
Multiply the terms
(2x2−5x)x2−12∣x∣
(2x2−5x)x2−12∣x∣=1
This equation equals 1 only if the base equals 1 or -1 or the exponent equals 0
2x2−5x=12x2−5x=−1x2−12∣x∣=0
Rewrite the expression
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Evaluate
2x2−5x=1
Move the expression to the left side
2x2−5x−1=0
Substitute a=2,b=−5 and c=−1 into the quadratic formula x=2a−b±b2−4ac
x=2×25±(−5)2−4×2(−1)
Simplify the expression
x=45±(−5)2−4×2(−1)
Simplify the expression
More Steps
Evaluate
(−5)2−4×2(−1)
Multiply
(−5)2−(−8)
Rewrite the expression
52−(−8)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
52+8
Evaluate the power
25+8
Add the numbers
33
x=45±33
Separate the equation into 2 possible cases
x=45+33x=45−33
x=45+33x=45−332x2−5x=−1x2−12∣x∣=0
Rewrite the expression
More Steps
Evaluate
2x2−5x=−1
Move the expression to the left side
2x2−5x−(−1)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x2−5x+1=0
Substitute a=2,b=−5 and c=1 into the quadratic formula x=2a−b±b2−4ac
x=2×25±(−5)2−4×2
Simplify the expression
x=45±(−5)2−4×2
Simplify the expression
More Steps
Evaluate
(−5)2−4×2
Multiply the numbers
(−5)2−8
Rewrite the expression
52−8
Evaluate the power
25−8
Subtract the numbers
17
x=45±17
Separate the equation into 2 possible cases
x=45+17x=45−17
x=45+33x=45−33x=45+17x=45−17x2−12∣x∣=0
Evaluate
More Steps
Evaluate
x2−12∣x∣=0
Separate the equation into 2 possible cases
x2−12x=0,x≥0x2−12(−x)=0,x<0
Solve the equation
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Evaluate
x2−12x=0
Factor the expression
x(x−12)=0
When the product of factors equals 0,at least one factor is 0
x=0x−12=0
Solve the equation for x
x=0x=12
x=0x=12,x≥0x2−12(−x)=0,x<0
Solve the equation
More Steps
Evaluate
x2−12(−x)=0
Calculate
x2+12x=0
Factor the expression
x(x+12)=0
When the product of factors equals 0,at least one factor is 0
x=0x+12=0
Solve the equation for x
x=0x=−12
x=0x=12,x≥0x=0x=−12,x<0
Find the intersection
x=0x=12x=0x=−12,x<0
Find the intersection
x=0x=12x=−12
x=45+33x=45−33x=45+17x=45−17x=0x=12x=−12
Solution
x1=−12,x2=45−33,x3=0,x4=45−17,x5=45+17,x6=45+33,x7=12
Alternative Form
x1=−12,x2≈−0.186141,x3=0,x4≈0.219224,x5≈2.280776,x6≈2.686141,x7=12
Show Solution
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