x^2+24x=9

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Solution for x^2+24x=9 equation:


Simplifying
x2 + 24x = 9

Reorder the terms:
24x + x2 = 9

Solving
24x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 24x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 24x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 24x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 24x + x2 = 0 + 9
24x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
24x + x2 = 9

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 = 9 + 144

Reorder the terms:
144 + 24x + x2 = 9 + 144

Combine like terms: 9 + 144 = 153
144 + 24x + x2 = 153

Factor a perfect square on the left side:
(x + 12)(x + 12) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + 12) equal to 12.369316877 and -12.369316877.

Subproblem 1

x + 12 = 12.369316877 Simplifying x + 12 = 12.369316877 Reorder the terms: 12 + x = 12.369316877 Solving 12 + x = 12.369316877 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 = 12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.369316877 + -12 x = 12.369316877 + -12 Combine like terms: 12.369316877 + -12 = 0.369316877 x = 0.369316877 Simplifying x = 0.369316877

Subproblem 2

x + 12 = -12.369316877 Simplifying x + 12 = -12.369316877 Reorder the terms: 12 + x = -12.369316877 Solving 12 + x = -12.369316877 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 = -12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.369316877 + -12 x = -12.369316877 + -12 Combine like terms: -12.369316877 + -12 = -24.369316877 x = -24.369316877 Simplifying x = -24.369316877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.369316877, -24.369316877}

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