x^2+24x+16=0

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Solution for x^2+24x+16=0 equation:


Simplifying
x2 + 24x + 16 = 0

Reorder the terms:
16 + 24x + x2 = 0

Solving
16 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 24x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 24x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 24x + x2 = 0 + -16
24x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
24x + x2 = -16

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 = -16 + 144

Reorder the terms:
144 + 24x + x2 = -16 + 144

Combine like terms: -16 + 144 = 128
144 + 24x + x2 = 128

Factor a perfect square on the left side:
(x + 12)(x + 12) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + 12) equal to 11.313708499 and -11.313708499.

Subproblem 1

x + 12 = 11.313708499 Simplifying x + 12 = 11.313708499 Reorder the terms: 12 + x = 11.313708499 Solving 12 + x = 11.313708499 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 = 11.313708499 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.313708499 + -12 x = 11.313708499 + -12 Combine like terms: 11.313708499 + -12 = -0.686291501 x = -0.686291501 Simplifying x = -0.686291501

Subproblem 2

x + 12 = -11.313708499 Simplifying x + 12 = -11.313708499 Reorder the terms: 12 + x = -11.313708499 Solving 12 + x = -11.313708499 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 = -11.313708499 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.313708499 + -12 x = -11.313708499 + -12 Combine like terms: -11.313708499 + -12 = -23.313708499 x = -23.313708499 Simplifying x = -23.313708499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.686291501, -23.313708499}

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