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Simplifying x2 + 18x = 15 Reorder the terms: 18x + x2 = 15 Solving 18x + x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 18x + x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 18x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 18x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 18x + x2 = 0 + 15 18x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 18x + x2 = 15 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 = 15 + 81 Reorder the terms: 81 + 18x + x2 = 15 + 81 Combine like terms: 15 + 81 = 96 81 + 18x + x2 = 96 Factor a perfect square on the left side: (x + 9)(x + 9) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 9) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 9 = 9.797958971 Simplifying x + 9 = 9.797958971 Reorder the terms: 9 + x = 9.797958971 Solving 9 + x = 9.797958971 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 = 9.797958971 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.797958971 + -9 x = 9.797958971 + -9 Combine like terms: 9.797958971 + -9 = 0.797958971 x = 0.797958971 Simplifying x = 0.797958971Subproblem 2
x + 9 = -9.797958971 Simplifying x + 9 = -9.797958971 Reorder the terms: 9 + x = -9.797958971 Solving 9 + x = -9.797958971 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 = -9.797958971 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.797958971 + -9 x = -9.797958971 + -9 Combine like terms: -9.797958971 + -9 = -18.797958971 x = -18.797958971 Simplifying x = -18.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.797958971, -18.797958971}
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