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Simplifying x2 + 12 = 18x Reorder the terms: 12 + x2 = 18x Solving 12 + x2 = 18x Solving for variable 'x'. Reorder the terms: 12 + -18x + x2 = 18x + -18x Combine like terms: 18x + -18x = 0 12 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -18x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -18x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -18x + x2 = 0 + -12 -18x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -18x + x2 = -12 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 = -12 + 81 Reorder the terms: 81 + -18x + x2 = -12 + 81 Combine like terms: -12 + 81 = 69 81 + -18x + x2 = 69 Factor a perfect square on the left side: (x + -9)(x + -9) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -9) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -9 = 8.306623863 Simplifying x + -9 = 8.306623863 Reorder the terms: -9 + x = 8.306623863 Solving -9 + x = 8.306623863 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 = 8.306623863 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.306623863 + 9 x = 8.306623863 + 9 Combine like terms: 8.306623863 + 9 = 17.306623863 x = 17.306623863 Simplifying x = 17.306623863Subproblem 2
x + -9 = -8.306623863 Simplifying x + -9 = -8.306623863 Reorder the terms: -9 + x = -8.306623863 Solving -9 + x = -8.306623863 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 = -8.306623863 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.306623863 + 9 x = -8.306623863 + 9 Combine like terms: -8.306623863 + 9 = 0.693376137 x = 0.693376137 Simplifying x = 0.693376137Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.306623863, 0.693376137}
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