X^2-8X-8=

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Solution for X^2-8X-8= equation:


Simplifying
X2 + -8X + -8 = 0

Reorder the terms:
-8 + -8X + X2 = 0

Solving
-8 + -8X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -8X + 8 + X2 = 0 + 8

Reorder the terms:
-8 + 8 + -8X + X2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -8X + X2 = 0 + 8
-8X + X2 = 0 + 8

Combine like terms: 0 + 8 = 8
-8X + X2 = 8

The X term is -8X.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8X + 16 + X2 = 8 + 16

Reorder the terms:
16 + -8X + X2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -8X + X2 = 24

Factor a perfect square on the left side:
(X + -4)(X + -4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(X + -4) equal to 4.898979486 and -4.898979486.

Subproblem 1

X + -4 = 4.898979486 Simplifying X + -4 = 4.898979486 Reorder the terms: -4 + X = 4.898979486 Solving -4 + X = 4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + X = 4.898979486 + 4 X = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 X = 8.898979486 Simplifying X = 8.898979486

Subproblem 2

X + -4 = -4.898979486 Simplifying X + -4 = -4.898979486 Reorder the terms: -4 + X = -4.898979486 Solving -4 + X = -4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + X = -4.898979486 + 4 X = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 X = -0.898979486 Simplifying X = -0.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. X = {8.898979486, -0.898979486}

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