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Simplifying 2x(18 + -1x) = 15 (18 * 2x + -1x * 2x) = 15 (36x + -2x2) = 15 Solving 36x + -2x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 36x + -2x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 36x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -18x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -18x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -18x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -18x + x2 = 0 + -7.5 -18x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -18x + x2 = -7.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -7.5 + 81 Reorder the terms: 81 + -18x + x2 = -7.5 + 81 Combine like terms: -7.5 + 81 = 73.5 81 + -18x + x2 = 73.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 73.5 Calculate the square root of the right side: 8.5732141 Break this problem into two subproblems by setting (x + -9) equal to 8.5732141 and -8.5732141.Subproblem 1
x + -9 = 8.5732141 Simplifying x + -9 = 8.5732141 Reorder the terms: -9 + x = 8.5732141 Solving -9 + x = 8.5732141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.5732141 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.5732141 + 9 x = 8.5732141 + 9 Combine like terms: 8.5732141 + 9 = 17.5732141 x = 17.5732141 Simplifying x = 17.5732141Subproblem 2
x + -9 = -8.5732141 Simplifying x + -9 = -8.5732141 Reorder the terms: -9 + x = -8.5732141 Solving -9 + x = -8.5732141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.5732141 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.5732141 + 9 x = -8.5732141 + 9 Combine like terms: -8.5732141 + 9 = 0.4267859 x = 0.4267859 Simplifying x = 0.4267859Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.5732141, 0.4267859}
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