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Simplifying 0 = x2 + 18x + 12 Reorder the terms: 0 = 12 + 18x + x2 Solving 0 = 12 + 18x + x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -18x + -1x2 = 12 + 18x + x2 + -12 + -18x + -1x2 Reorder the terms: -12 + -18x + -1x2 = 12 + -12 + 18x + -18x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2 -12 + -18x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -12 + -18x + -1x2 = 0 + x2 + -1x2 -12 + -18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -18x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 18x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 18x + x2)' equal to zero and attempt to solve: Simplifying 12 + 18x + x2 = 0 Solving 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 = -0.693376137 x = -0.693376137 Simplifying x = -0.693376137Subproblem 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 = -17.306623863 x = -17.306623863 Simplifying x = -17.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.693376137, -17.306623863}Solution
x = {-0.693376137, -17.306623863}
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