x^2+x^2-8x+16=256

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Solution for x^2+x^2-8x+16=256 equation:


Simplifying
x2 + x2 + -8x + 16 = 256

Reorder the terms:
16 + -8x + x2 + x2 = 256

Combine like terms: x2 + x2 = 2x2
16 + -8x + 2x2 = 256

Solving
16 + -8x + 2x2 = 256

Solving for variable 'x'.

Reorder the terms:
16 + -256 + -8x + 2x2 = 256 + -256

Combine like terms: 16 + -256 = -240
-240 + -8x + 2x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-240 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-120 + -4x + x2)' equal to zero and attempt to solve: Simplifying -120 + -4x + x2 = 0 Solving -120 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -4x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -4x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -4x + x2 = 0 + 120 -4x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -4x + x2 = 120 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 120 + 4 Reorder the terms: 4 + -4x + x2 = 120 + 4 Combine like terms: 120 + 4 = 124 4 + -4x + x2 = 124 Factor a perfect square on the left side: (x + -2)(x + -2) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + -2) equal to 11.135528726 and -11.135528726.

Subproblem 1

x + -2 = 11.135528726 Simplifying x + -2 = 11.135528726 Reorder the terms: -2 + x = 11.135528726 Solving -2 + x = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.135528726 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.135528726 + 2 x = 11.135528726 + 2 Combine like terms: 11.135528726 + 2 = 13.135528726 x = 13.135528726 Simplifying x = 13.135528726

Subproblem 2

x + -2 = -11.135528726 Simplifying x + -2 = -11.135528726 Reorder the terms: -2 + x = -11.135528726 Solving -2 + x = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.135528726 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.135528726 + 2 x = -11.135528726 + 2 Combine like terms: -11.135528726 + 2 = -9.135528726 x = -9.135528726 Simplifying x = -9.135528726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.135528726, -9.135528726}

Solution

x = {13.135528726, -9.135528726}

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