4x^2+24x+9=121

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Solution for 4x^2+24x+9=121 equation: 


Simplifying
4x2 + 24x + 9 = 121

Reorder the terms:
9 + 24x + 4x2 = 121

Solving
9 + 24x + 4x2 = 121

Solving for variable 'x'.

Reorder the terms:
9 + -121 + 24x + 4x2 = 121 + -121

Combine like terms: 9 + -121 = -112
-112 + 24x + 4x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-112 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + 6x + x2 = 0

Solving
-28 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 6x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 6x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 6x + x2 = 0 + 28
6x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
6x + x2 = 28

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 = 28 + 9

Reorder the terms:
9 + 6x + x2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + 6x + x2 = 37

Factor a perfect square on the left side:
(x + 3)(x + 3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 3) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + 3 = 6.08276253

Simplifying
x + 3 = 6.08276253

Reorder the terms:
3 + x = 6.08276253

Solving
3 + x = 6.08276253

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 = 6.08276253 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.08276253 + -3
x = 6.08276253 + -3

Combine like terms: 6.08276253 + -3 = 3.08276253
x = 3.08276253

Simplifying
x = 3.08276253


Subproblem 2
x + 3 = -6.08276253

Simplifying
x + 3 = -6.08276253

Reorder the terms:
3 + x = -6.08276253

Solving
3 + x = -6.08276253

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 = -6.08276253 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.08276253 + -3
x = -6.08276253 + -3

Combine like terms: -6.08276253 + -3 = -9.08276253
x = -9.08276253

Simplifying
x = -9.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.08276253, -9.08276253}
Solution
x = {3.08276253, -9.08276253}

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