x^2-8x+4=90

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Solution for x^2-8x+4=90 equation:


Simplifying
x2 + -8x + 4 = 90

Reorder the terms:
4 + -8x + x2 = 90

Solving
4 + -8x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
4 + -90 + -8x + x2 = 90 + -90

Combine like terms: 4 + -90 = -86
-86 + -8x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-86 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '86' to each side of the equation.
-86 + -8x + 86 + x2 = 0 + 86

Reorder the terms:
-86 + 86 + -8x + x2 = 0 + 86

Combine like terms: -86 + 86 = 0
0 + -8x + x2 = 0 + 86
-8x + x2 = 0 + 86

Combine like terms: 0 + 86 = 86
-8x + x2 = 86

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 = 86 + 16

Reorder the terms:
16 + -8x + x2 = 86 + 16

Combine like terms: 86 + 16 = 102
16 + -8x + x2 = 102

Factor a perfect square on the left side:
(x + -4)(x + -4) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -4) equal to 10.099504938 and -10.099504938.

Subproblem 1

x + -4 = 10.099504938 Simplifying x + -4 = 10.099504938 Reorder the terms: -4 + x = 10.099504938 Solving -4 + x = 10.099504938 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 = 10.099504938 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.099504938 + 4 x = 10.099504938 + 4 Combine like terms: 10.099504938 + 4 = 14.099504938 x = 14.099504938 Simplifying x = 14.099504938

Subproblem 2

x + -4 = -10.099504938 Simplifying x + -4 = -10.099504938 Reorder the terms: -4 + x = -10.099504938 Solving -4 + x = -10.099504938 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 = -10.099504938 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.099504938 + 4 x = -10.099504938 + 4 Combine like terms: -10.099504938 + 4 = -6.099504938 x = -6.099504938 Simplifying x = -6.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.099504938, -6.099504938}

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