12x+96(x+6)(x+6)=0

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Solution for 12x+96(x+6)(x+6)=0 equation:


Simplifying
12x + 96(x + 6)(x + 6) = 0

Reorder the terms:
12x + 96(6 + x)(x + 6) = 0

Reorder the terms:
12x + 96(6 + x)(6 + x) = 0

Multiply (6 + x) * (6 + x)
12x + 96(6(6 + x) + x(6 + x)) = 0
12x + 96((6 * 6 + x * 6) + x(6 + x)) = 0
12x + 96((36 + 6x) + x(6 + x)) = 0
12x + 96(36 + 6x + (6 * x + x * x)) = 0
12x + 96(36 + 6x + (6x + x2)) = 0

Combine like terms: 6x + 6x = 12x
12x + 96(36 + 12x + x2) = 0
12x + (36 * 96 + 12x * 96 + x2 * 96) = 0
12x + (3456 + 1152x + 96x2) = 0

Reorder the terms:
3456 + 12x + 1152x + 96x2 = 0

Combine like terms: 12x + 1152x = 1164x
3456 + 1164x + 96x2 = 0

Solving
3456 + 1164x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(288 + 97x + 8x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(288 + 97x + 8x2)' equal to zero and attempt to solve: Simplifying 288 + 97x + 8x2 = 0 Solving 288 + 97x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 36 + 12.125x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + 12.125x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 12.125x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 12.125x + x2 = 0 + -36 12.125x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 12.125x + x2 = -36 The x term is 12.125x. Take half its coefficient (6.0625). Square it (36.75390625) and add it to both sides. Add '36.75390625' to each side of the equation. 12.125x + 36.75390625 + x2 = -36 + 36.75390625 Reorder the terms: 36.75390625 + 12.125x + x2 = -36 + 36.75390625 Combine like terms: -36 + 36.75390625 = 0.75390625 36.75390625 + 12.125x + x2 = 0.75390625 Factor a perfect square on the left side: (x + 6.0625)(x + 6.0625) = 0.75390625 Calculate the square root of the right side: 0.868277749 Break this problem into two subproblems by setting (x + 6.0625) equal to 0.868277749 and -0.868277749.

Subproblem 1

x + 6.0625 = 0.868277749 Simplifying x + 6.0625 = 0.868277749 Reorder the terms: 6.0625 + x = 0.868277749 Solving 6.0625 + x = 0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.0625' to each side of the equation. 6.0625 + -6.0625 + x = 0.868277749 + -6.0625 Combine like terms: 6.0625 + -6.0625 = 0.0000 0.0000 + x = 0.868277749 + -6.0625 x = 0.868277749 + -6.0625 Combine like terms: 0.868277749 + -6.0625 = -5.194222251 x = -5.194222251 Simplifying x = -5.194222251

Subproblem 2

x + 6.0625 = -0.868277749 Simplifying x + 6.0625 = -0.868277749 Reorder the terms: 6.0625 + x = -0.868277749 Solving 6.0625 + x = -0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.0625' to each side of the equation. 6.0625 + -6.0625 + x = -0.868277749 + -6.0625 Combine like terms: 6.0625 + -6.0625 = 0.0000 0.0000 + x = -0.868277749 + -6.0625 x = -0.868277749 + -6.0625 Combine like terms: -0.868277749 + -6.0625 = -6.930777749 x = -6.930777749 Simplifying x = -6.930777749

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.194222251, -6.930777749}

Solution

x = {-5.194222251, -6.930777749}

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