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Simplifying x2 + 18x + 68 = 0 Reorder the terms: 68 + 18x + x2 = 0 Solving 68 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + 18x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + 18x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + 18x + x2 = 0 + -68 18x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 18x + x2 = -68 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 = -68 + 81 Reorder the terms: 81 + 18x + x2 = -68 + 81 Combine like terms: -68 + 81 = 13 81 + 18x + x2 = 13 Factor a perfect square on the left side: (x + 9)(x + 9) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 9) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 9 = 3.605551275 Simplifying x + 9 = 3.605551275 Reorder the terms: 9 + x = 3.605551275 Solving 9 + x = 3.605551275 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 = 3.605551275 + -9 Combine like terms: 9 + -9 = 0 0 + x = 3.605551275 + -9 x = 3.605551275 + -9 Combine like terms: 3.605551275 + -9 = -5.394448725 x = -5.394448725 Simplifying x = -5.394448725Subproblem 2
x + 9 = -3.605551275 Simplifying x + 9 = -3.605551275 Reorder the terms: 9 + x = -3.605551275 Solving 9 + x = -3.605551275 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 = -3.605551275 + -9 Combine like terms: 9 + -9 = 0 0 + x = -3.605551275 + -9 x = -3.605551275 + -9 Combine like terms: -3.605551275 + -9 = -12.605551275 x = -12.605551275 Simplifying x = -12.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.394448725, -12.605551275}
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