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Simplifying 3x(x + 8) = 180 Reorder the terms: 3x(8 + x) = 180 (8 * 3x + x * 3x) = 180 (24x + 3x2) = 180 Solving 24x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 24x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + 8x + x2)' equal to zero and attempt to solve: Simplifying -60 + 8x + x2 = 0 Solving -60 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 8x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 8x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 8x + x2 = 0 + 60 8x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 8x + x2 = 60 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 60 + 16 Reorder the terms: 16 + 8x + x2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + 8x + x2 = 76 Factor a perfect square on the left side: (x + 4)(x + 4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + 4) equal to 8.717797887 and -8.717797887.Subproblem 1
x + 4 = 8.717797887 Simplifying x + 4 = 8.717797887 Reorder the terms: 4 + x = 8.717797887 Solving 4 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.717797887 + -4 x = 8.717797887 + -4 Combine like terms: 8.717797887 + -4 = 4.717797887 x = 4.717797887 Simplifying x = 4.717797887Subproblem 2
x + 4 = -8.717797887 Simplifying x + 4 = -8.717797887 Reorder the terms: 4 + x = -8.717797887 Solving 4 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.717797887 + -4 x = -8.717797887 + -4 Combine like terms: -8.717797887 + -4 = -12.717797887 x = -12.717797887 Simplifying x = -12.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.717797887, -12.717797887}Solution
x = {4.717797887, -12.717797887}
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