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Simplifying x2 + -18x + -10 = 0 Reorder the terms: -10 + -18x + x2 = 0 Solving -10 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -18x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -18x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -18x + x2 = 0 + 10 -18x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -18x + x2 = 10 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 = 10 + 81 Reorder the terms: 81 + -18x + x2 = 10 + 81 Combine like terms: 10 + 81 = 91 81 + -18x + x2 = 91 Factor a perfect square on the left side: (x + -9)(x + -9) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -9) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -9 = 9.539392014 Simplifying x + -9 = 9.539392014 Reorder the terms: -9 + x = 9.539392014 Solving -9 + x = 9.539392014 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 = 9.539392014 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.539392014 + 9 x = 9.539392014 + 9 Combine like terms: 9.539392014 + 9 = 18.539392014 x = 18.539392014 Simplifying x = 18.539392014Subproblem 2
x + -9 = -9.539392014 Simplifying x + -9 = -9.539392014 Reorder the terms: -9 + x = -9.539392014 Solving -9 + x = -9.539392014 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 = -9.539392014 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.539392014 + 9 x = -9.539392014 + 9 Combine like terms: -9.539392014 + 9 = -0.539392014 x = -0.539392014 Simplifying x = -0.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.539392014, -0.539392014}
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