x^2-24x=-32

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Solution for x^2-24x=-32 equation:


Simplifying
x2 + -24x = -32

Reorder the terms:
-24x + x2 = -32

Solving
-24x + x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -24x + x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -24x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -24x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -24x + x2 = 0 + -32
-24x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-24x + x2 = -32

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -32 + 144

Reorder the terms:
144 + -24x + x2 = -32 + 144

Combine like terms: -32 + 144 = 112
144 + -24x + x2 = 112

Factor a perfect square on the left side:
(x + -12)(x + -12) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -12) equal to 10.583005244 and -10.583005244.

Subproblem 1

x + -12 = 10.583005244 Simplifying x + -12 = 10.583005244 Reorder the terms: -12 + x = 10.583005244 Solving -12 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.583005244 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.583005244 + 12 x = 10.583005244 + 12 Combine like terms: 10.583005244 + 12 = 22.583005244 x = 22.583005244 Simplifying x = 22.583005244

Subproblem 2

x + -12 = -10.583005244 Simplifying x + -12 = -10.583005244 Reorder the terms: -12 + x = -10.583005244 Solving -12 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.583005244 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.583005244 + 12 x = -10.583005244 + 12 Combine like terms: -10.583005244 + 12 = 1.416994756 x = 1.416994756 Simplifying x = 1.416994756

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.583005244, 1.416994756}

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