Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=23−17,x2=1,x3=2,x4=23+17
Alternative Form
x1≈−0.561553,x2=1,x3=2,x4≈3.561553
Evaluate
∣x−3∣×2∣x×1∣=4
Simplify
More Steps
Evaluate
∣x−3∣×2∣x×1∣
Any expression multiplied by 1 remains the same
∣x−3∣×2∣x∣
Multiply the first two terms
2∣x−3∣∣x∣
Multiply the terms
2∣x(x−3)∣
2∣x(x−3)∣=4
Divide both sides
22∣x(x−3)∣=24
Divide the numbers
∣x(x−3)∣=24
Divide the numbers
More Steps
Evaluate
24
Reduce the numbers
12
Calculate
2
∣x(x−3)∣=2
Separate the equation into 2 possible cases
x(x−3)=2x(x−3)=−2
Solve the equation for x
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Evaluate
x(x−3)=2
Expand the expression
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Evaluate
x(x−3)
Apply the distributive property
x×x−x×3
Multiply the terms
x2−x×3
Use the commutative property to reorder the terms
x2−3x
x2−3x=2
Move the expression to the left side
x2−3x−2=0
Substitute a=1,b=−3 and c=−2 into the quadratic formula x=2a−b±b2−4ac
x=23±(−3)2−4(−2)
Simplify the expression
More Steps
Evaluate
(−3)2−4(−2)
Multiply the numbers
(−3)2−(−8)
Rewrite the expression
32−(−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
32+8
Evaluate the power
9+8
Add the numbers
17
x=23±17
Separate the equation into 2 possible cases
x=23+17x=23−17
x=23+17x=23−17x(x−3)=−2
Solve the equation for x
More Steps
Evaluate
x(x−3)=−2
Expand the expression
More Steps
Evaluate
x(x−3)
Apply the distributive property
x×x−x×3
Multiply the terms
x2−x×3
Use the commutative property to reorder the terms
x2−3x
x2−3x=−2
Move the expression to the left side
x2−3x−(−2)=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
x2−3x+2=0
Factor the expression
More Steps
Evaluate
x2−3x+2
Rewrite the expression
x2+(−1−2)x+2
Calculate
x2−x−2x+2
Rewrite the expression
x×x−x−2x+2
Factor out x from the expression
x(x−1)−2x+2
Factor out −2 from the expression
x(x−1)−2(x−1)
Factor out x−1 from the expression
(x−2)(x−1)
(x−2)(x−1)=0
When the product of factors equals 0,at least one factor is 0
x−2=0x−1=0
Solve the equation for x
More Steps
Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x−1=0
Solve the equation for x
More Steps
Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=2x=1
x=23+17x=23−17x=2x=1
Solution
x1=23−17,x2=1,x3=2,x4=23+17
Alternative Form
x1≈−0.561553,x2=1,x3=2,x4≈3.561553
Show Solution
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