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Simplifying (14 + 2x)(20 + 2x) + (14)(20)(x) = 832 Multiply (14 + 2x) * (20 + 2x) (14(20 + 2x) + 2x * (20 + 2x)) + (14)(20)(x) = 832 ((20 * 14 + 2x * 14) + 2x * (20 + 2x)) + (14)(20)(x) = 832 ((280 + 28x) + 2x * (20 + 2x)) + (14)(20)(x) = 832 (280 + 28x + (20 * 2x + 2x * 2x)) + (14)(20)(x) = 832 (280 + 28x + (40x + 4x2)) + (14)(20)(x) = 832 Combine like terms: 28x + 40x = 68x (280 + 68x + 4x2) + (14)(20)(x) = 832 Multiply 14 * 20 280 + 68x + 4x2 + 280x = 832 Reorder the terms: 280 + 68x + 280x + 4x2 = 832 Combine like terms: 68x + 280x = 348x 280 + 348x + 4x2 = 832 Solving 280 + 348x + 4x2 = 832 Solving for variable 'x'. Reorder the terms: 280 + -832 + 348x + 4x2 = 832 + -832 Combine like terms: 280 + -832 = -552 -552 + 348x + 4x2 = 832 + -832 Combine like terms: 832 + -832 = 0 -552 + 348x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-138 + 87x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-138 + 87x + x2)' equal to zero and attempt to solve: Simplifying -138 + 87x + x2 = 0 Solving -138 + 87x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 87x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 87x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 87x + x2 = 0 + 138 87x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 87x + x2 = 138 The x term is 87x. Take half its coefficient (43.5). Square it (1892.25) and add it to both sides. Add '1892.25' to each side of the equation. 87x + 1892.25 + x2 = 138 + 1892.25 Reorder the terms: 1892.25 + 87x + x2 = 138 + 1892.25 Combine like terms: 138 + 1892.25 = 2030.25 1892.25 + 87x + x2 = 2030.25 Factor a perfect square on the left side: (x + 43.5)(x + 43.5) = 2030.25 Calculate the square root of the right side: 45.058295574 Break this problem into two subproblems by setting (x + 43.5) equal to 45.058295574 and -45.058295574.Subproblem 1
x + 43.5 = 45.058295574 Simplifying x + 43.5 = 45.058295574 Reorder the terms: 43.5 + x = 45.058295574 Solving 43.5 + x = 45.058295574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43.5' to each side of the equation. 43.5 + -43.5 + x = 45.058295574 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + x = 45.058295574 + -43.5 x = 45.058295574 + -43.5 Combine like terms: 45.058295574 + -43.5 = 1.558295574 x = 1.558295574 Simplifying x = 1.558295574Subproblem 2
x + 43.5 = -45.058295574 Simplifying x + 43.5 = -45.058295574 Reorder the terms: 43.5 + x = -45.058295574 Solving 43.5 + x = -45.058295574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43.5' to each side of the equation. 43.5 + -43.5 + x = -45.058295574 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + x = -45.058295574 + -43.5 x = -45.058295574 + -43.5 Combine like terms: -45.058295574 + -43.5 = -88.558295574 x = -88.558295574 Simplifying x = -88.558295574Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.558295574, -88.558295574}Solution
x = {1.558295574, -88.558295574}
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