x^2-120x-475=0

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Solution for x^2-120x-475=0 equation:


Simplifying
x2 + -120x + -475 = 0

Reorder the terms:
-475 + -120x + x2 = 0

Solving
-475 + -120x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '475' to each side of the equation.
-475 + -120x + 475 + x2 = 0 + 475

Reorder the terms:
-475 + 475 + -120x + x2 = 0 + 475

Combine like terms: -475 + 475 = 0
0 + -120x + x2 = 0 + 475
-120x + x2 = 0 + 475

Combine like terms: 0 + 475 = 475
-120x + x2 = 475

The x term is -120x.  Take half its coefficient (-60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
-120x + 3600 + x2 = 475 + 3600

Reorder the terms:
3600 + -120x + x2 = 475 + 3600

Combine like terms: 475 + 3600 = 4075
3600 + -120x + x2 = 4075

Factor a perfect square on the left side:
(x + -60)(x + -60) = 4075

Calculate the square root of the right side: 63.835726674

Break this problem into two subproblems by setting 
(x + -60) equal to 63.835726674 and -63.835726674.

Subproblem 1

x + -60 = 63.835726674 Simplifying x + -60 = 63.835726674 Reorder the terms: -60 + x = 63.835726674 Solving -60 + x = 63.835726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 63.835726674 + 60 Combine like terms: -60 + 60 = 0 0 + x = 63.835726674 + 60 x = 63.835726674 + 60 Combine like terms: 63.835726674 + 60 = 123.835726674 x = 123.835726674 Simplifying x = 123.835726674

Subproblem 2

x + -60 = -63.835726674 Simplifying x + -60 = -63.835726674 Reorder the terms: -60 + x = -63.835726674 Solving -60 + x = -63.835726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -63.835726674 + 60 Combine like terms: -60 + 60 = 0 0 + x = -63.835726674 + 60 x = -63.835726674 + 60 Combine like terms: -63.835726674 + 60 = -3.835726674 x = -3.835726674 Simplifying x = -3.835726674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {123.835726674, -3.835726674}

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