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Simplifying 18x3 + -8x2 + -14x = 0 Reorder the terms: -14x + -8x2 + 18x3 = 0 Solving -14x + -8x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + -4x + 9x2) = 0 Ignore the factor 2.Subproblem 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 '(-7 + -4x + 9x2)' equal to zero and attempt to solve: Simplifying -7 + -4x + 9x2 = 0 Solving -7 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -0.4444444444x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -0.4444444444x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + 0.7777777778 -0.4444444444x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -0.4444444444x + x2 = 0.7777777778 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 0.7777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 0.7777777778 + 0.04938271604 Combine like terms: 0.7777777778 + 0.04938271604 = 0.82716049384 0.04938271604 + -0.4444444444x + x2 = 0.82716049384 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 0.82716049384 Calculate the square root of the right side: 0.909483641 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 0.909483641 and -0.909483641.Subproblem 1
x + -0.2222222222 = 0.909483641 Simplifying x + -0.2222222222 = 0.909483641 Reorder the terms: -0.2222222222 + x = 0.909483641 Solving -0.2222222222 + x = 0.909483641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 0.909483641 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.909483641 + 0.2222222222 x = 0.909483641 + 0.2222222222 Combine like terms: 0.909483641 + 0.2222222222 = 1.1317058632 x = 1.1317058632 Simplifying x = 1.1317058632Subproblem 2
x + -0.2222222222 = -0.909483641 Simplifying x + -0.2222222222 = -0.909483641 Reorder the terms: -0.2222222222 + x = -0.909483641 Solving -0.2222222222 + x = -0.909483641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -0.909483641 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.909483641 + 0.2222222222 x = -0.909483641 + 0.2222222222 Combine like terms: -0.909483641 + 0.2222222222 = -0.6872614188 x = -0.6872614188 Simplifying x = -0.6872614188Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1317058632, -0.6872614188}Solution
x = {0, 1.1317058632, -0.6872614188}
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