x^2-8x-171=0

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Solution for x^2-8x-171=0 equation:


Simplifying
x2 + -8x + -171 = 0

Reorder the terms:
-171 + -8x + x2 = 0

Solving
-171 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '171' to each side of the equation.
-171 + -8x + 171 + x2 = 0 + 171

Reorder the terms:
-171 + 171 + -8x + x2 = 0 + 171

Combine like terms: -171 + 171 = 0
0 + -8x + x2 = 0 + 171
-8x + x2 = 0 + 171

Combine like terms: 0 + 171 = 171
-8x + x2 = 171

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 = 171 + 16

Reorder the terms:
16 + -8x + x2 = 171 + 16

Combine like terms: 171 + 16 = 187
16 + -8x + x2 = 187

Factor a perfect square on the left side:
(x + -4)(x + -4) = 187

Calculate the square root of the right side: 13.674794331

Break this problem into two subproblems by setting 
(x + -4) equal to 13.674794331 and -13.674794331.

Subproblem 1

x + -4 = 13.674794331 Simplifying x + -4 = 13.674794331 Reorder the terms: -4 + x = 13.674794331 Solving -4 + x = 13.674794331 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 = 13.674794331 + 4 Combine like terms: -4 + 4 = 0 0 + x = 13.674794331 + 4 x = 13.674794331 + 4 Combine like terms: 13.674794331 + 4 = 17.674794331 x = 17.674794331 Simplifying x = 17.674794331

Subproblem 2

x + -4 = -13.674794331 Simplifying x + -4 = -13.674794331 Reorder the terms: -4 + x = -13.674794331 Solving -4 + x = -13.674794331 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 = -13.674794331 + 4 Combine like terms: -4 + 4 = 0 0 + x = -13.674794331 + 4 x = -13.674794331 + 4 Combine like terms: -13.674794331 + 4 = -9.674794331 x = -9.674794331 Simplifying x = -9.674794331

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.674794331, -9.674794331}

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