135-124x+x^2=

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Solution for 135-124x+x^2= equation:


Simplifying
135 + -124x + x2 = 0

Solving
135 + -124x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-135' to each side of the equation.
135 + -124x + -135 + x2 = 0 + -135

Reorder the terms:
135 + -135 + -124x + x2 = 0 + -135

Combine like terms: 135 + -135 = 0
0 + -124x + x2 = 0 + -135
-124x + x2 = 0 + -135

Combine like terms: 0 + -135 = -135
-124x + x2 = -135

The x term is -124x.  Take half its coefficient (-62).
Square it (3844) and add it to both sides.

Add '3844' to each side of the equation.
-124x + 3844 + x2 = -135 + 3844

Reorder the terms:
3844 + -124x + x2 = -135 + 3844

Combine like terms: -135 + 3844 = 3709
3844 + -124x + x2 = 3709

Factor a perfect square on the left side:
(x + -62)(x + -62) = 3709

Calculate the square root of the right side: 60.901559914

Break this problem into two subproblems by setting 
(x + -62) equal to 60.901559914 and -60.901559914.

Subproblem 1

x + -62 = 60.901559914 Simplifying x + -62 = 60.901559914 Reorder the terms: -62 + x = 60.901559914 Solving -62 + x = 60.901559914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62' to each side of the equation. -62 + 62 + x = 60.901559914 + 62 Combine like terms: -62 + 62 = 0 0 + x = 60.901559914 + 62 x = 60.901559914 + 62 Combine like terms: 60.901559914 + 62 = 122.901559914 x = 122.901559914 Simplifying x = 122.901559914

Subproblem 2

x + -62 = -60.901559914 Simplifying x + -62 = -60.901559914 Reorder the terms: -62 + x = -60.901559914 Solving -62 + x = -60.901559914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62' to each side of the equation. -62 + 62 + x = -60.901559914 + 62 Combine like terms: -62 + 62 = 0 0 + x = -60.901559914 + 62 x = -60.901559914 + 62 Combine like terms: -60.901559914 + 62 = 1.098440086 x = 1.098440086 Simplifying x = 1.098440086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {122.901559914, 1.098440086}

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