x^2-6x+9=126.5625

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Solution for x^2-6x+9=126.5625 equation:


Simplifying
x2 + -6x + 9 = 126.5625

Reorder the terms:
9 + -6x + x2 = 126.5625

Solving
9 + -6x + x2 = 126.5625

Solving for variable 'x'.

Reorder the terms:
9 + -126.5625 + -6x + x2 = 126.5625 + -126.5625

Combine like terms: 9 + -126.5625 = -117.5625
-117.5625 + -6x + x2 = 126.5625 + -126.5625

Combine like terms: 126.5625 + -126.5625 = 0.0000
-117.5625 + -6x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '117.5625' to each side of the equation.
-117.5625 + -6x + 117.5625 + x2 = 0.0000 + 117.5625

Reorder the terms:
-117.5625 + 117.5625 + -6x + x2 = 0.0000 + 117.5625

Combine like terms: -117.5625 + 117.5625 = 0.0000
0.0000 + -6x + x2 = 0.0000 + 117.5625
-6x + x2 = 0.0000 + 117.5625

Combine like terms: 0.0000 + 117.5625 = 117.5625
-6x + x2 = 117.5625

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 117.5625 + 9

Reorder the terms:
9 + -6x + x2 = 117.5625 + 9

Combine like terms: 117.5625 + 9 = 126.5625
9 + -6x + x2 = 126.5625

Factor a perfect square on the left side:
(x + -3)(x + -3) = 126.5625

Calculate the square root of the right side: 11.25

Break this problem into two subproblems by setting 
(x + -3) equal to 11.25 and -11.25.

Subproblem 1

x + -3 = 11.25 Simplifying x + -3 = 11.25 Reorder the terms: -3 + x = 11.25 Solving -3 + x = 11.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 11.25 + 3 Combine like terms: -3 + 3 = 0 0 + x = 11.25 + 3 x = 11.25 + 3 Combine like terms: 11.25 + 3 = 14.25 x = 14.25 Simplifying x = 14.25

Subproblem 2

x + -3 = -11.25 Simplifying x + -3 = -11.25 Reorder the terms: -3 + x = -11.25 Solving -3 + x = -11.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -11.25 + 3 Combine like terms: -3 + 3 = 0 0 + x = -11.25 + 3 x = -11.25 + 3 Combine like terms: -11.25 + 3 = -8.25 x = -8.25 Simplifying x = -8.25

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.25, -8.25}

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