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Simplifying x2 + 18x = 180 Reorder the terms: 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 = 7.155494421 x = 7.155494421 Simplifying x = 7.155494421Subproblem 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 = -25.155494421 x = -25.155494421 Simplifying x = -25.155494421Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.155494421, -25.155494421}
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