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Simplifying 2x + x(x + -20) = 180 Reorder the terms: 2x + x(-20 + x) = 180 2x + (-20 * x + x * x) = 180 2x + (-20x + x2) = 180 Combine like terms: 2x + -20x = -18x -18x + x2 = 180 Solving -18x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -18x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -18x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -18x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -18x + x2 = 0 + 180 -18x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -18x + x2 = 180 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 = 180 + 81 Reorder the terms: 81 + -18x + x2 = 180 + 81 Combine like terms: 180 + 81 = 261 81 + -18x + x2 = 261 Factor a perfect square on the left side: (x + -9)(x + -9) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (x + -9) equal to 16.155494421 and -16.155494421.Subproblem 1
x + -9 = 16.155494421 Simplifying x + -9 = 16.155494421 Reorder the terms: -9 + x = 16.155494421 Solving -9 + x = 16.155494421 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 = 16.155494421 + 9 Combine like terms: -9 + 9 = 0 0 + x = 16.155494421 + 9 x = 16.155494421 + 9 Combine like terms: 16.155494421 + 9 = 25.155494421 x = 25.155494421 Simplifying x = 25.155494421Subproblem 2
x + -9 = -16.155494421 Simplifying x + -9 = -16.155494421 Reorder the terms: -9 + x = -16.155494421 Solving -9 + x = -16.155494421 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 = -16.155494421 + 9 Combine like terms: -9 + 9 = 0 0 + x = -16.155494421 + 9 x = -16.155494421 + 9 Combine like terms: -16.155494421 + 9 = -7.155494421 x = -7.155494421 Simplifying x = -7.155494421Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.155494421, -7.155494421}
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