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Simplifying x2 + 18x + -136 = 0 Reorder the terms: -136 + 18x + x2 = 0 Solving -136 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 18x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 18x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 18x + x2 = 0 + 136 18x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 18x + x2 = 136 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 = 136 + 81 Reorder the terms: 81 + 18x + x2 = 136 + 81 Combine like terms: 136 + 81 = 217 81 + 18x + x2 = 217 Factor a perfect square on the left side: (x + 9)(x + 9) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 9) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 9 = 14.730919863 Simplifying x + 9 = 14.730919863 Reorder the terms: 9 + x = 14.730919863 Solving 9 + x = 14.730919863 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 = 14.730919863 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.730919863 + -9 x = 14.730919863 + -9 Combine like terms: 14.730919863 + -9 = 5.730919863 x = 5.730919863 Simplifying x = 5.730919863Subproblem 2
x + 9 = -14.730919863 Simplifying x + 9 = -14.730919863 Reorder the terms: 9 + x = -14.730919863 Solving 9 + x = -14.730919863 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 = -14.730919863 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.730919863 + -9 x = -14.730919863 + -9 Combine like terms: -14.730919863 + -9 = -23.730919863 x = -23.730919863 Simplifying x = -23.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.730919863, -23.730919863}
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