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Simplifying x2 + 18x + -102 = 0 Reorder the terms: -102 + 18x + x2 = 0 Solving -102 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 18x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 18x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 18x + x2 = 0 + 102 18x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 18x + x2 = 102 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 = 102 + 81 Reorder the terms: 81 + 18x + x2 = 102 + 81 Combine like terms: 102 + 81 = 183 81 + 18x + x2 = 183 Factor a perfect square on the left side: (x + 9)(x + 9) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (x + 9) equal to 13.527749258 and -13.527749258.Subproblem 1
x + 9 = 13.527749258 Simplifying x + 9 = 13.527749258 Reorder the terms: 9 + x = 13.527749258 Solving 9 + x = 13.527749258 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 = 13.527749258 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.527749258 + -9 x = 13.527749258 + -9 Combine like terms: 13.527749258 + -9 = 4.527749258 x = 4.527749258 Simplifying x = 4.527749258Subproblem 2
x + 9 = -13.527749258 Simplifying x + 9 = -13.527749258 Reorder the terms: 9 + x = -13.527749258 Solving 9 + x = -13.527749258 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 = -13.527749258 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.527749258 + -9 x = -13.527749258 + -9 Combine like terms: -13.527749258 + -9 = -22.527749258 x = -22.527749258 Simplifying x = -22.527749258Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.527749258, -22.527749258}
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