x^2-176x-121=0

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Solution for x^2-176x-121=0 equation:


Simplifying
x2 + -176x + -121 = 0

Reorder the terms:
-121 + -176x + x2 = 0

Solving
-121 + -176x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + -176x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + -176x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + -176x + x2 = 0 + 121
-176x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
-176x + x2 = 121

The x term is -176x.  Take half its coefficient (-88).
Square it (7744) and add it to both sides.

Add '7744' to each side of the equation.
-176x + 7744 + x2 = 121 + 7744

Reorder the terms:
7744 + -176x + x2 = 121 + 7744

Combine like terms: 121 + 7744 = 7865
7744 + -176x + x2 = 7865

Factor a perfect square on the left side:
(x + -88)(x + -88) = 7865

Calculate the square root of the right side: 88.684835231

Break this problem into two subproblems by setting 
(x + -88) equal to 88.684835231 and -88.684835231.

Subproblem 1

x + -88 = 88.684835231 Simplifying x + -88 = 88.684835231 Reorder the terms: -88 + x = 88.684835231 Solving -88 + x = 88.684835231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + x = 88.684835231 + 88 Combine like terms: -88 + 88 = 0 0 + x = 88.684835231 + 88 x = 88.684835231 + 88 Combine like terms: 88.684835231 + 88 = 176.684835231 x = 176.684835231 Simplifying x = 176.684835231

Subproblem 2

x + -88 = -88.684835231 Simplifying x + -88 = -88.684835231 Reorder the terms: -88 + x = -88.684835231 Solving -88 + x = -88.684835231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + x = -88.684835231 + 88 Combine like terms: -88 + 88 = 0 0 + x = -88.684835231 + 88 x = -88.684835231 + 88 Combine like terms: -88.684835231 + 88 = -0.684835231 x = -0.684835231 Simplifying x = -0.684835231

Solution

The solution to the problem is based on the solutions from the subproblems. x = {176.684835231, -0.684835231}

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