Question
Simplify the expression
x2−8x−84
Evaluate
(x−4)2−100
Expand the expression
x2−8x+16−100
Solution
x2−8x−84
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Factor the expression
(x−14)(x+6)
Evaluate
(x−4)2−100
Rewrite the expression in exponential form
(x−4)2−102
Use a2−b2=(a−b)(a+b) to factor the expression
(x−4−10)(x−4+10)
Evaluate
(x−14)(x−4+10)
Solution
(x−14)(x+6)
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Find the roots
x1=−6,x2=14
Evaluate
(x−4)2−100
To find the roots of the expression,set the expression equal to 0
(x−4)2−100=0
Move the constant to the right-hand side and change its sign
(x−4)2=0+100
Removing 0 doesn't change the value,so remove it from the expression
(x−4)2=100
Take the root of both sides of the equation and remember to use both positive and negative roots
x−4=±100
Simplify the expression
More Steps

Evaluate
100
Write the number in exponential form with the base of 10
102
Reduce the index of the radical and exponent with 2
10
x−4=±10
Separate the equation into 2 possible cases
x−4=10x−4=−10
Calculate
More Steps

Evaluate
x−4=10
Move the constant to the right-hand side and change its sign
x=10+4
Add the numbers
x=14
x=14x−4=−10
Calculate
More Steps

Evaluate
x−4=−10
Move the constant to the right-hand side and change its sign
x=−10+4
Add the numbers
x=−6
x=14x=−6
Solution
x1=−6,x2=14
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