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Simplifying x2 + 18x = -19 Reorder the terms: 18x + x2 = -19 Solving 18x + x2 = -19 Solving for variable 'x'. Reorder the terms: 19 + 18x + x2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 18x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 18x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 18x + x2 = 0 + -19 18x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 18x + x2 = -19 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 = -19 + 81 Reorder the terms: 81 + 18x + x2 = -19 + 81 Combine like terms: -19 + 81 = 62 81 + 18x + x2 = 62 Factor a perfect square on the left side: (x + 9)(x + 9) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + 9) equal to 7.874007874 and -7.874007874.Subproblem 1
x + 9 = 7.874007874 Simplifying x + 9 = 7.874007874 Reorder the terms: 9 + x = 7.874007874 Solving 9 + x = 7.874007874 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 = 7.874007874 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.874007874 + -9 x = 7.874007874 + -9 Combine like terms: 7.874007874 + -9 = -1.125992126 x = -1.125992126 Simplifying x = -1.125992126Subproblem 2
x + 9 = -7.874007874 Simplifying x + 9 = -7.874007874 Reorder the terms: 9 + x = -7.874007874 Solving 9 + x = -7.874007874 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 = -7.874007874 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.874007874 + -9 x = -7.874007874 + -9 Combine like terms: -7.874007874 + -9 = -16.874007874 x = -16.874007874 Simplifying x = -16.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.125992126, -16.874007874}
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