x^2-18x-71=0

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Solution for x^2-18x-71=0 equation:


Simplifying
x2 + -18x + -71 = 0

Reorder the terms:
-71 + -18x + x2 = 0

Solving
-71 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + -18x + 71 + x2 = 0 + 71

Reorder the terms:
-71 + 71 + -18x + x2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + -18x + x2 = 0 + 71
-18x + x2 = 0 + 71

Combine like terms: 0 + 71 = 71
-18x + x2 = 71

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 71 + 81

Reorder the terms:
81 + -18x + x2 = 71 + 81

Combine like terms: 71 + 81 = 152
81 + -18x + x2 = 152

Factor a perfect square on the left side:
(x + -9)(x + -9) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(x + -9) equal to 12.328828006 and -12.328828006.

Subproblem 1

x + -9 = 12.328828006 Simplifying x + -9 = 12.328828006 Reorder the terms: -9 + x = 12.328828006 Solving -9 + x = 12.328828006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 12.328828006 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.328828006 + 9 x = 12.328828006 + 9 Combine like terms: 12.328828006 + 9 = 21.328828006 x = 21.328828006 Simplifying x = 21.328828006

Subproblem 2

x + -9 = -12.328828006 Simplifying x + -9 = -12.328828006 Reorder the terms: -9 + x = -12.328828006 Solving -9 + x = -12.328828006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -12.328828006 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.328828006 + 9 x = -12.328828006 + 9 Combine like terms: -12.328828006 + 9 = -3.328828006 x = -3.328828006 Simplifying x = -3.328828006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.328828006, -3.328828006}

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