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Simplifying (14 + 2x)(20 + 2x) + -1(14)(20)(x) = 832 Multiply (14 + 2x) * (20 + 2x) (14(20 + 2x) + 2x * (20 + 2x)) + -1(14)(20)(x) = 832 ((20 * 14 + 2x * 14) + 2x * (20 + 2x)) + -1(14)(20)(x) = 832 ((280 + 28x) + 2x * (20 + 2x)) + -1(14)(20)(x) = 832 (280 + 28x + (20 * 2x + 2x * 2x)) + -1(14)(20)(x) = 832 (280 + 28x + (40x + 4x2)) + -1(14)(20)(x) = 832 Combine like terms: 28x + 40x = 68x (280 + 68x + 4x2) + -1(14)(20)(x) = 832 Multiply -1 * 14 280 + 68x + 4x2 + -14 * 20x = 832 Multiply -14 * 20 280 + 68x + 4x2 + -280x = 832 Reorder the terms: 280 + 68x + -280x + 4x2 = 832 Combine like terms: 68x + -280x = -212x 280 + -212x + 4x2 = 832 Solving 280 + -212x + 4x2 = 832 Solving for variable 'x'. Reorder the terms: 280 + -832 + -212x + 4x2 = 832 + -832 Combine like terms: 280 + -832 = -552 -552 + -212x + 4x2 = 832 + -832 Combine like terms: 832 + -832 = 0 -552 + -212x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-138 + -53x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-138 + -53x + x2)' equal to zero and attempt to solve: Simplifying -138 + -53x + x2 = 0 Solving -138 + -53x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + -53x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + -53x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + -53x + x2 = 0 + 138 -53x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 -53x + x2 = 138 The x term is -53x. Take half its coefficient (-26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. -53x + 702.25 + x2 = 138 + 702.25 Reorder the terms: 702.25 + -53x + x2 = 138 + 702.25 Combine like terms: 138 + 702.25 = 840.25 702.25 + -53x + x2 = 840.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 840.25 Calculate the square root of the right side: 28.987066081 Break this problem into two subproblems by setting (x + -26.5) equal to 28.987066081 and -28.987066081.Subproblem 1
x + -26.5 = 28.987066081 Simplifying x + -26.5 = 28.987066081 Reorder the terms: -26.5 + x = 28.987066081 Solving -26.5 + x = 28.987066081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = 28.987066081 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 28.987066081 + 26.5 x = 28.987066081 + 26.5 Combine like terms: 28.987066081 + 26.5 = 55.487066081 x = 55.487066081 Simplifying x = 55.487066081Subproblem 2
x + -26.5 = -28.987066081 Simplifying x + -26.5 = -28.987066081 Reorder the terms: -26.5 + x = -28.987066081 Solving -26.5 + x = -28.987066081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = -28.987066081 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -28.987066081 + 26.5 x = -28.987066081 + 26.5 Combine like terms: -28.987066081 + 26.5 = -2.487066081 x = -2.487066081 Simplifying x = -2.487066081Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.487066081, -2.487066081}Solution
x = {55.487066081, -2.487066081}
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