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Simplifying x2 + 18x + -416 = 0 Reorder the terms: -416 + 18x + x2 = 0 Solving -416 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '416' to each side of the equation. -416 + 18x + 416 + x2 = 0 + 416 Reorder the terms: -416 + 416 + 18x + x2 = 0 + 416 Combine like terms: -416 + 416 = 0 0 + 18x + x2 = 0 + 416 18x + x2 = 0 + 416 Combine like terms: 0 + 416 = 416 18x + x2 = 416 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 = 416 + 81 Reorder the terms: 81 + 18x + x2 = 416 + 81 Combine like terms: 416 + 81 = 497 81 + 18x + x2 = 497 Factor a perfect square on the left side: (x + 9)(x + 9) = 497 Calculate the square root of the right side: 22.29349681 Break this problem into two subproblems by setting (x + 9) equal to 22.29349681 and -22.29349681.Subproblem 1
x + 9 = 22.29349681 Simplifying x + 9 = 22.29349681 Reorder the terms: 9 + x = 22.29349681 Solving 9 + x = 22.29349681 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 = 22.29349681 + -9 Combine like terms: 9 + -9 = 0 0 + x = 22.29349681 + -9 x = 22.29349681 + -9 Combine like terms: 22.29349681 + -9 = 13.29349681 x = 13.29349681 Simplifying x = 13.29349681Subproblem 2
x + 9 = -22.29349681 Simplifying x + 9 = -22.29349681 Reorder the terms: 9 + x = -22.29349681 Solving 9 + x = -22.29349681 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 = -22.29349681 + -9 Combine like terms: 9 + -9 = 0 0 + x = -22.29349681 + -9 x = -22.29349681 + -9 Combine like terms: -22.29349681 + -9 = -31.29349681 x = -31.29349681 Simplifying x = -31.29349681Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.29349681, -31.29349681}
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