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Simplifying x(2x + -15) = 180 Reorder the terms: x(-15 + 2x) = 180 (-15 * x + 2x * x) = 180 (-15x + 2x2) = 180 Solving -15x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -15x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -90 + -7.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -7.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -7.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -7.5x + x2 = 0 + 90 -7.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -7.5x + x2 = 90 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 90 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 90 + 14.0625 Combine like terms: 90 + 14.0625 = 104.0625 14.0625 + -7.5x + x2 = 104.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 104.0625 Calculate the square root of the right side: 10.201102882 Break this problem into two subproblems by setting (x + -3.75) equal to 10.201102882 and -10.201102882.Subproblem 1
x + -3.75 = 10.201102882 Simplifying x + -3.75 = 10.201102882 Reorder the terms: -3.75 + x = 10.201102882 Solving -3.75 + x = 10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 10.201102882 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 10.201102882 + 3.75 x = 10.201102882 + 3.75 Combine like terms: 10.201102882 + 3.75 = 13.951102882 x = 13.951102882 Simplifying x = 13.951102882Subproblem 2
x + -3.75 = -10.201102882 Simplifying x + -3.75 = -10.201102882 Reorder the terms: -3.75 + x = -10.201102882 Solving -3.75 + x = -10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -10.201102882 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -10.201102882 + 3.75 x = -10.201102882 + 3.75 Combine like terms: -10.201102882 + 3.75 = -6.451102882 x = -6.451102882 Simplifying x = -6.451102882Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.951102882, -6.451102882}
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