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Simplifying x2 + 18x = -7 Reorder the terms: 18x + x2 = -7 Solving 18x + x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 18x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 18x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 18x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 18x + x2 = 0 + -7 18x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 18x + x2 = -7 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 = -7 + 81 Reorder the terms: 81 + 18x + x2 = -7 + 81 Combine like terms: -7 + 81 = 74 81 + 18x + x2 = 74 Factor a perfect square on the left side: (x + 9)(x + 9) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + 9) equal to 8.602325267 and -8.602325267.Subproblem 1
x + 9 = 8.602325267 Simplifying x + 9 = 8.602325267 Reorder the terms: 9 + x = 8.602325267 Solving 9 + x = 8.602325267 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 = 8.602325267 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.602325267 + -9 x = 8.602325267 + -9 Combine like terms: 8.602325267 + -9 = -0.397674733 x = -0.397674733 Simplifying x = -0.397674733Subproblem 2
x + 9 = -8.602325267 Simplifying x + 9 = -8.602325267 Reorder the terms: 9 + x = -8.602325267 Solving 9 + x = -8.602325267 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 = -8.602325267 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.602325267 + -9 x = -8.602325267 + -9 Combine like terms: -8.602325267 + -9 = -17.602325267 x = -17.602325267 Simplifying x = -17.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.397674733, -17.602325267}
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