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Simplifying (4x + -12)(4x + -12) = 24 Reorder the terms: (-12 + 4x)(4x + -12) = 24 Reorder the terms: (-12 + 4x)(-12 + 4x) = 24 Multiply (-12 + 4x) * (-12 + 4x) (-12(-12 + 4x) + 4x * (-12 + 4x)) = 24 ((-12 * -12 + 4x * -12) + 4x * (-12 + 4x)) = 24 ((144 + -48x) + 4x * (-12 + 4x)) = 24 (144 + -48x + (-12 * 4x + 4x * 4x)) = 24 (144 + -48x + (-48x + 16x2)) = 24 Combine like terms: -48x + -48x = -96x (144 + -96x + 16x2) = 24 Solving 144 + -96x + 16x2 = 24 Solving for variable 'x'. Reorder the terms: 144 + -24 + -96x + 16x2 = 24 + -24 Combine like terms: 144 + -24 = 120 120 + -96x + 16x2 = 24 + -24 Combine like terms: 24 + -24 = 0 120 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(15 + -12x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -12x + 2x2 = 0 Solving 15 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -6x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -6x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -6x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -6x + x2 = 0 + -7.5 -6x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -6x + x2 = -7.5 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 = -7.5 + 9 Reorder the terms: 9 + -6x + x2 = -7.5 + 9 Combine like terms: -7.5 + 9 = 1.5 9 + -6x + x2 = 1.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -3) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -3 = 1.224744871 Simplifying x + -3 = 1.224744871 Reorder the terms: -3 + x = 1.224744871 Solving -3 + x = 1.224744871 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 = 1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.224744871 + 3 x = 1.224744871 + 3 Combine like terms: 1.224744871 + 3 = 4.224744871 x = 4.224744871 Simplifying x = 4.224744871Subproblem 2
x + -3 = -1.224744871 Simplifying x + -3 = -1.224744871 Reorder the terms: -3 + x = -1.224744871 Solving -3 + x = -1.224744871 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 = -1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.224744871 + 3 x = -1.224744871 + 3 Combine like terms: -1.224744871 + 3 = 1.775255129 x = 1.775255129 Simplifying x = 1.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.224744871, 1.775255129}Solution
x = {4.224744871, 1.775255129}
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