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Simplifying (4x + -3)(2x + -6) = 500 Reorder the terms: (-3 + 4x)(2x + -6) = 500 Reorder the terms: (-3 + 4x)(-6 + 2x) = 500 Multiply (-3 + 4x) * (-6 + 2x) (-3(-6 + 2x) + 4x * (-6 + 2x)) = 500 ((-6 * -3 + 2x * -3) + 4x * (-6 + 2x)) = 500 ((18 + -6x) + 4x * (-6 + 2x)) = 500 (18 + -6x + (-6 * 4x + 2x * 4x)) = 500 (18 + -6x + (-24x + 8x2)) = 500 Combine like terms: -6x + -24x = -30x (18 + -30x + 8x2) = 500 Solving 18 + -30x + 8x2 = 500 Solving for variable 'x'. Reorder the terms: 18 + -500 + -30x + 8x2 = 500 + -500 Combine like terms: 18 + -500 = -482 -482 + -30x + 8x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -482 + -30x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-241 + -15x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-241 + -15x + 4x2)' equal to zero and attempt to solve: Simplifying -241 + -15x + 4x2 = 0 Solving -241 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -60.25 + -3.75x + x2 = 0 Move the constant term to the right: Add '60.25' to each side of the equation. -60.25 + -3.75x + 60.25 + x2 = 0 + 60.25 Reorder the terms: -60.25 + 60.25 + -3.75x + x2 = 0 + 60.25 Combine like terms: -60.25 + 60.25 = 0.00 0.00 + -3.75x + x2 = 0 + 60.25 -3.75x + x2 = 0 + 60.25 Combine like terms: 0 + 60.25 = 60.25 -3.75x + x2 = 60.25 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 60.25 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 60.25 + 3.515625 Combine like terms: 60.25 + 3.515625 = 63.765625 3.515625 + -3.75x + x2 = 63.765625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 63.765625 Calculate the square root of the right side: 7.985338127 Break this problem into two subproblems by setting (x + -1.875) equal to 7.985338127 and -7.985338127.Subproblem 1
x + -1.875 = 7.985338127 Simplifying x + -1.875 = 7.985338127 Reorder the terms: -1.875 + x = 7.985338127 Solving -1.875 + x = 7.985338127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 7.985338127 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 7.985338127 + 1.875 x = 7.985338127 + 1.875 Combine like terms: 7.985338127 + 1.875 = 9.860338127 x = 9.860338127 Simplifying x = 9.860338127Subproblem 2
x + -1.875 = -7.985338127 Simplifying x + -1.875 = -7.985338127 Reorder the terms: -1.875 + x = -7.985338127 Solving -1.875 + x = -7.985338127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -7.985338127 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -7.985338127 + 1.875 x = -7.985338127 + 1.875 Combine like terms: -7.985338127 + 1.875 = -6.110338127 x = -6.110338127 Simplifying x = -6.110338127Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.860338127, -6.110338127}Solution
x = {9.860338127, -6.110338127}
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