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Simplifying x(4x + 32) = 12 Reorder the terms: x(32 + 4x) = 12 (32 * x + 4x * x) = 12 (32x + 4x2) = 12 Solving 32x + 4x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 32x + 4x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 8x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 8x + x2)' equal to zero and attempt to solve: Simplifying -3 + 8x + x2 = 0 Solving -3 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8x + x2 = 0 + 3 8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 8x + x2 = 3 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 3 + 16 Reorder the terms: 16 + 8x + x2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8x + x2 = 19 Factor a perfect square on the left side: (x + 4)(x + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 4 = 4.358898944 Simplifying x + 4 = 4.358898944 Reorder the terms: 4 + x = 4.358898944 Solving 4 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.358898944 + -4 x = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 x = 0.358898944 Simplifying x = 0.358898944Subproblem 2
x + 4 = -4.358898944 Simplifying x + 4 = -4.358898944 Reorder the terms: 4 + x = -4.358898944 Solving 4 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.358898944 + -4 x = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 x = -8.358898944 Simplifying x = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.358898944, -8.358898944}Solution
x = {0.358898944, -8.358898944}
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