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Simplifying 4(4x + -3) * 6x = 9x + -12 Reorder the terms: 4(-3 + 4x) * 6x = 9x + -12 Reorder the terms for easier multiplication: 4 * 6x(-3 + 4x) = 9x + -12 Multiply 4 * 6 24x(-3 + 4x) = 9x + -12 (-3 * 24x + 4x * 24x) = 9x + -12 (-72x + 96x2) = 9x + -12 Reorder the terms: -72x + 96x2 = -12 + 9x Solving -72x + 96x2 = -12 + 9x Solving for variable 'x'. Reorder the terms: 12 + -72x + -9x + 96x2 = -12 + 9x + 12 + -9x Combine like terms: -72x + -9x = -81x 12 + -81x + 96x2 = -12 + 9x + 12 + -9x Reorder the terms: 12 + -81x + 96x2 = -12 + 12 + 9x + -9x Combine like terms: -12 + 12 = 0 12 + -81x + 96x2 = 0 + 9x + -9x 12 + -81x + 96x2 = 9x + -9x Combine like terms: 9x + -9x = 0 12 + -81x + 96x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -27x + 32x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -27x + 32x2)' equal to zero and attempt to solve: Simplifying 4 + -27x + 32x2 = 0 Solving 4 + -27x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.125 + -0.84375x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.84375x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.84375x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.84375x + x2 = 0 + -0.125 -0.84375x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.84375x + x2 = -0.125 The x term is -0.84375x. Take half its coefficient (-0.421875). Square it (0.1779785156) and add it to both sides. Add '0.1779785156' to each side of the equation. -0.84375x + 0.1779785156 + x2 = -0.125 + 0.1779785156 Reorder the terms: 0.1779785156 + -0.84375x + x2 = -0.125 + 0.1779785156 Combine like terms: -0.125 + 0.1779785156 = 0.0529785156 0.1779785156 + -0.84375x + x2 = 0.0529785156 Factor a perfect square on the left side: (x + -0.421875)(x + -0.421875) = 0.0529785156 Calculate the square root of the right side: 0.230170623 Break this problem into two subproblems by setting (x + -0.421875) equal to 0.230170623 and -0.230170623.Subproblem 1
x + -0.421875 = 0.230170623 Simplifying x + -0.421875 = 0.230170623 Reorder the terms: -0.421875 + x = 0.230170623 Solving -0.421875 + x = 0.230170623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.421875' to each side of the equation. -0.421875 + 0.421875 + x = 0.230170623 + 0.421875 Combine like terms: -0.421875 + 0.421875 = 0.000000 0.000000 + x = 0.230170623 + 0.421875 x = 0.230170623 + 0.421875 Combine like terms: 0.230170623 + 0.421875 = 0.652045623 x = 0.652045623 Simplifying x = 0.652045623Subproblem 2
x + -0.421875 = -0.230170623 Simplifying x + -0.421875 = -0.230170623 Reorder the terms: -0.421875 + x = -0.230170623 Solving -0.421875 + x = -0.230170623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.421875' to each side of the equation. -0.421875 + 0.421875 + x = -0.230170623 + 0.421875 Combine like terms: -0.421875 + 0.421875 = 0.000000 0.000000 + x = -0.230170623 + 0.421875 x = -0.230170623 + 0.421875 Combine like terms: -0.230170623 + 0.421875 = 0.191704377 x = 0.191704377 Simplifying x = 0.191704377Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.652045623, 0.191704377}Solution
x = {0.652045623, 0.191704377}
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