Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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x1=−27,x2=211
Alternative Form
x1=−3.5,x2=5.5
Evaluate
4(x−1)2−81=0
Expand the expression
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Evaluate
4(x−1)2−81
Expand the expression
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Evaluate
4(x−1)2
Expand the expression
4(x2−2x+1)
Apply the distributive property
4x2−4×2x+4×1
Multiply the numbers
4x2−8x+4×1
Any expression multiplied by 1 remains the same
4x2−8x+4
4x2−8x+4−81
Subtract the numbers
4x2−8x−77
4x2−8x−77=0
Factor the expression
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Evaluate
4x2−8x−77
Rewrite the expression
4x2+(14−22)x−77
Calculate
4x2+14x−22x−77
Rewrite the expression
2x×2x+2x×7−11×2x−11×7
Factor out 2x from the expression
2x(2x+7)−11×2x−11×7
Factor out −11 from the expression
2x(2x+7)−11(2x+7)
Factor out 2x+7 from the expression
(2x−11)(2x+7)
(2x−11)(2x+7)=0
When the product of factors equals 0,at least one factor is 0
2x−11=02x+7=0
Solve the equation for x
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Evaluate
2x−11=0
Move the constant to the right-hand side and change its sign
2x=0+11
Removing 0 doesn't change the value,so remove it from the expression
2x=11
Divide both sides
22x=211
Divide the numbers
x=211
x=2112x+7=0
Solve the equation for x
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Evaluate
2x+7=0
Move the constant to the right-hand side and change its sign
2x=0−7
Removing 0 doesn't change the value,so remove it from the expression
2x=−7
Divide both sides
22x=2−7
Divide the numbers
x=2−7
Use b−a=−ba=−ba to rewrite the fraction
x=−27
x=211x=−27
Solution
x1=−27,x2=211
Alternative Form
x1=−3.5,x2=5.5
Show Solution
