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Simplifying x2 + -18x = 8 Reorder the terms: -18x + x2 = 8 Solving -18x + x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -18x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -18x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -18x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -18x + x2 = 0 + 8 -18x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -18x + x2 = 8 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 = 8 + 81 Reorder the terms: 81 + -18x + x2 = 8 + 81 Combine like terms: 8 + 81 = 89 81 + -18x + x2 = 89 Factor a perfect square on the left side: (x + -9)(x + -9) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -9) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -9 = 9.433981132 Simplifying x + -9 = 9.433981132 Reorder the terms: -9 + x = 9.433981132 Solving -9 + x = 9.433981132 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 = 9.433981132 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.433981132 + 9 x = 9.433981132 + 9 Combine like terms: 9.433981132 + 9 = 18.433981132 x = 18.433981132 Simplifying x = 18.433981132Subproblem 2
x + -9 = -9.433981132 Simplifying x + -9 = -9.433981132 Reorder the terms: -9 + x = -9.433981132 Solving -9 + x = -9.433981132 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 = -9.433981132 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.433981132 + 9 x = -9.433981132 + 9 Combine like terms: -9.433981132 + 9 = -0.433981132 x = -0.433981132 Simplifying x = -0.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.433981132, -0.433981132}
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