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Simplifying x3 + 18x2 + 18x = 0 Reorder the terms: 18x + 18x2 + x3 = 0 Solving 18x + 18x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(18 + 18x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(18 + 18x + x2)' equal to zero and attempt to solve: Simplifying 18 + 18x + x2 = 0 Solving 18 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 18x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 18x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 18x + x2 = 0 + -18 18x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 18x + x2 = -18 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 = -18 + 81 Reorder the terms: 81 + 18x + x2 = -18 + 81 Combine like terms: -18 + 81 = 63 81 + 18x + x2 = 63 Factor a perfect square on the left side: (x + 9)(x + 9) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 9) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 9 = 7.937253933 Simplifying x + 9 = 7.937253933 Reorder the terms: 9 + x = 7.937253933 Solving 9 + x = 7.937253933 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 = 7.937253933 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.937253933 + -9 x = 7.937253933 + -9 Combine like terms: 7.937253933 + -9 = -1.062746067 x = -1.062746067 Simplifying x = -1.062746067Subproblem 2
x + 9 = -7.937253933 Simplifying x + 9 = -7.937253933 Reorder the terms: 9 + x = -7.937253933 Solving 9 + x = -7.937253933 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 = -7.937253933 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.937253933 + -9 x = -7.937253933 + -9 Combine like terms: -7.937253933 + -9 = -16.937253933 x = -16.937253933 Simplifying x = -16.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.062746067, -16.937253933}Solution
x = {0, -1.062746067, -16.937253933}
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