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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 = 17.602325267 x = 17.602325267 Simplifying x = 17.602325267Subproblem 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 = 0.397674733 x = 0.397674733 Simplifying x = 0.397674733Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.602325267, 0.397674733}
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