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Simplifying x2 + 18x + -156 = 0 Reorder the terms: -156 + 18x + x2 = 0 Solving -156 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + 18x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + 18x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 18x + x2 = 0 + 156 18x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 18x + x2 = 156 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 = 156 + 81 Reorder the terms: 81 + 18x + x2 = 156 + 81 Combine like terms: 156 + 81 = 237 81 + 18x + x2 = 237 Factor a perfect square on the left side: (x + 9)(x + 9) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 9) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 9 = 15.394804318 Simplifying x + 9 = 15.394804318 Reorder the terms: 9 + x = 15.394804318 Solving 9 + x = 15.394804318 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 = 15.394804318 + -9 Combine like terms: 9 + -9 = 0 0 + x = 15.394804318 + -9 x = 15.394804318 + -9 Combine like terms: 15.394804318 + -9 = 6.394804318 x = 6.394804318 Simplifying x = 6.394804318Subproblem 2
x + 9 = -15.394804318 Simplifying x + 9 = -15.394804318 Reorder the terms: 9 + x = -15.394804318 Solving 9 + x = -15.394804318 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 = -15.394804318 + -9 Combine like terms: 9 + -9 = 0 0 + x = -15.394804318 + -9 x = -15.394804318 + -9 Combine like terms: -15.394804318 + -9 = -24.394804318 x = -24.394804318 Simplifying x = -24.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.394804318, -24.394804318}
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