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Simplifying 36(6x + 1) * 36(-1x + -13) = 30(5x + -3) * 30(x) Reorder the terms: 36(1 + 6x) * 36(-1x + -13) = 30(5x + -3) * 30(x) Reorder the terms: 36(1 + 6x) * 36(-13 + -1x) = 30(5x + -3) * 30(x) Reorder the terms for easier multiplication: 36 * 36(1 + 6x)(-13 + -1x) = 30(5x + -3) * 30(x) Multiply 36 * 36 1296(1 + 6x)(-13 + -1x) = 30(5x + -3) * 30(x) Multiply (1 + 6x) * (-13 + -1x) 1296(1(-13 + -1x) + 6x * (-13 + -1x)) = 30(5x + -3) * 30(x) 1296((-13 * 1 + -1x * 1) + 6x * (-13 + -1x)) = 30(5x + -3) * 30(x) 1296((-13 + -1x) + 6x * (-13 + -1x)) = 30(5x + -3) * 30(x) 1296(-13 + -1x + (-13 * 6x + -1x * 6x)) = 30(5x + -3) * 30(x) 1296(-13 + -1x + (-78x + -6x2)) = 30(5x + -3) * 30(x) Combine like terms: -1x + -78x = -79x 1296(-13 + -79x + -6x2) = 30(5x + -3) * 30(x) (-13 * 1296 + -79x * 1296 + -6x2 * 1296) = 30(5x + -3) * 30(x) (-16848 + -102384x + -7776x2) = 30(5x + -3) * 30(x) Reorder the terms: -16848 + -102384x + -7776x2 = 30(-3 + 5x) * 30(x) Reorder the terms for easier multiplication: -16848 + -102384x + -7776x2 = 30 * 30x(-3 + 5x) Multiply 30 * 30 -16848 + -102384x + -7776x2 = 900x(-3 + 5x) -16848 + -102384x + -7776x2 = (-3 * 900x + 5x * 900x) -16848 + -102384x + -7776x2 = (-2700x + 4500x2) Solving -16848 + -102384x + -7776x2 = -2700x + 4500x2 Solving for variable 'x'. Reorder the terms: -16848 + -102384x + 2700x + -7776x2 + -4500x2 = -2700x + 4500x2 + 2700x + -4500x2 Combine like terms: -102384x + 2700x = -99684x -16848 + -99684x + -7776x2 + -4500x2 = -2700x + 4500x2 + 2700x + -4500x2 Combine like terms: -7776x2 + -4500x2 = -12276x2 -16848 + -99684x + -12276x2 = -2700x + 4500x2 + 2700x + -4500x2 Reorder the terms: -16848 + -99684x + -12276x2 = -2700x + 2700x + 4500x2 + -4500x2 Combine like terms: -2700x + 2700x = 0 -16848 + -99684x + -12276x2 = 0 + 4500x2 + -4500x2 -16848 + -99684x + -12276x2 = 4500x2 + -4500x2 Combine like terms: 4500x2 + -4500x2 = 0 -16848 + -99684x + -12276x2 = 0 Factor out the Greatest Common Factor (GCF), '-36'. -36(468 + 2769x + 341x2) = 0 Ignore the factor -36.Subproblem 1
Set the factor '(468 + 2769x + 341x2)' equal to zero and attempt to solve: Simplifying 468 + 2769x + 341x2 = 0 Solving 468 + 2769x + 341x2 = 0 Begin completing the square. Divide all terms by 341 the coefficient of the squared term: Divide each side by '341'. 1.372434018 + 8.120234604x + x2 = 0 Move the constant term to the right: Add '-1.372434018' to each side of the equation. 1.372434018 + 8.120234604x + -1.372434018 + x2 = 0 + -1.372434018 Reorder the terms: 1.372434018 + -1.372434018 + 8.120234604x + x2 = 0 + -1.372434018 Combine like terms: 1.372434018 + -1.372434018 = 0.000000000 0.000000000 + 8.120234604x + x2 = 0 + -1.372434018 8.120234604x + x2 = 0 + -1.372434018 Combine like terms: 0 + -1.372434018 = -1.372434018 8.120234604x + x2 = -1.372434018 The x term is 8.120234604x. Take half its coefficient (4.060117302). Square it (16.48455251) and add it to both sides. Add '16.48455251' to each side of the equation. 8.120234604x + 16.48455251 + x2 = -1.372434018 + 16.48455251 Reorder the terms: 16.48455251 + 8.120234604x + x2 = -1.372434018 + 16.48455251 Combine like terms: -1.372434018 + 16.48455251 = 15.112118492 16.48455251 + 8.120234604x + x2 = 15.112118492 Factor a perfect square on the left side: (x + 4.060117302)(x + 4.060117302) = 15.112118492 Calculate the square root of the right side: 3.887430834 Break this problem into two subproblems by setting (x + 4.060117302) equal to 3.887430834 and -3.887430834.Subproblem 1
x + 4.060117302 = 3.887430834 Simplifying x + 4.060117302 = 3.887430834 Reorder the terms: 4.060117302 + x = 3.887430834 Solving 4.060117302 + x = 3.887430834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.060117302' to each side of the equation. 4.060117302 + -4.060117302 + x = 3.887430834 + -4.060117302 Combine like terms: 4.060117302 + -4.060117302 = 0.000000000 0.000000000 + x = 3.887430834 + -4.060117302 x = 3.887430834 + -4.060117302 Combine like terms: 3.887430834 + -4.060117302 = -0.172686468 x = -0.172686468 Simplifying x = -0.172686468Subproblem 2
x + 4.060117302 = -3.887430834 Simplifying x + 4.060117302 = -3.887430834 Reorder the terms: 4.060117302 + x = -3.887430834 Solving 4.060117302 + x = -3.887430834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.060117302' to each side of the equation. 4.060117302 + -4.060117302 + x = -3.887430834 + -4.060117302 Combine like terms: 4.060117302 + -4.060117302 = 0.000000000 0.000000000 + x = -3.887430834 + -4.060117302 x = -3.887430834 + -4.060117302 Combine like terms: -3.887430834 + -4.060117302 = -7.947548136 x = -7.947548136 Simplifying x = -7.947548136Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.172686468, -7.947548136}Solution
x = {-0.172686468, -7.947548136}
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