(x-8)(x-8)=45

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Solution for (x-8)(x-8)=45 equation:


Simplifying
(x + -8)(x + -8) = 45

Reorder the terms:
(-8 + x)(x + -8) = 45

Reorder the terms:
(-8 + x)(-8 + x) = 45

Multiply (-8 + x) * (-8 + x)
(-8(-8 + x) + x(-8 + x)) = 45
((-8 * -8 + x * -8) + x(-8 + x)) = 45
((64 + -8x) + x(-8 + x)) = 45
(64 + -8x + (-8 * x + x * x)) = 45
(64 + -8x + (-8x + x2)) = 45

Combine like terms: -8x + -8x = -16x
(64 + -16x + x2) = 45

Solving
64 + -16x + x2 = 45

Solving for variable 'x'.

Reorder the terms:
64 + -45 + -16x + x2 = 45 + -45

Combine like terms: 64 + -45 = 19
19 + -16x + x2 = 45 + -45

Combine like terms: 45 + -45 = 0
19 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -16x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + -16x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -16x + x2 = 0 + -19
-16x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-16x + x2 = -19

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -19 + 64

Reorder the terms:
64 + -16x + x2 = -19 + 64

Combine like terms: -19 + 64 = 45
64 + -16x + x2 = 45

Factor a perfect square on the left side:
(x + -8)(x + -8) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -8) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + -8 = 6.708203933 Simplifying x + -8 = 6.708203933 Reorder the terms: -8 + x = 6.708203933 Solving -8 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 6.708203933 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.708203933 + 8 x = 6.708203933 + 8 Combine like terms: 6.708203933 + 8 = 14.708203933 x = 14.708203933 Simplifying x = 14.708203933

Subproblem 2

x + -8 = -6.708203933 Simplifying x + -8 = -6.708203933 Reorder the terms: -8 + x = -6.708203933 Solving -8 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -6.708203933 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.708203933 + 8 x = -6.708203933 + 8 Combine like terms: -6.708203933 + 8 = 1.291796067 x = 1.291796067 Simplifying x = 1.291796067

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.708203933, 1.291796067}

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