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Simplifying 18x3 + 16x2 + -10x = 0 Reorder the terms: -10x + 16x2 + 18x3 = 0 Solving -10x + 16x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + 8x + 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 '(-5 + 8x + 9x2)' equal to zero and attempt to solve: Simplifying -5 + 8x + 9x2 = 0 Solving -5 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.8888888889x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.8888888889x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + 0.5555555556 0.8888888889x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.8888888889x + x2 = 0.5555555556 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 0.5555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 0.5555555556 + 0.1975308642 Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198 0.1975308642 + 0.8888888889x + x2 = 0.7530864198 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.7530864198 Calculate the square root of the right side: 0.86780552 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.86780552 and -0.86780552.Subproblem 1
x + 0.4444444445 = 0.86780552 Simplifying x + 0.4444444445 = 0.86780552 Reorder the terms: 0.4444444445 + x = 0.86780552 Solving 0.4444444445 + x = 0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.86780552 + -0.4444444445 x = 0.86780552 + -0.4444444445 Combine like terms: 0.86780552 + -0.4444444445 = 0.4233610755 x = 0.4233610755 Simplifying x = 0.4233610755Subproblem 2
x + 0.4444444445 = -0.86780552 Simplifying x + 0.4444444445 = -0.86780552 Reorder the terms: 0.4444444445 + x = -0.86780552 Solving 0.4444444445 + x = -0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.86780552 + -0.4444444445 x = -0.86780552 + -0.4444444445 Combine like terms: -0.86780552 + -0.4444444445 = -1.3122499645 x = -1.3122499645 Simplifying x = -1.3122499645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4233610755, -1.3122499645}Solution
x = {0, 0.4233610755, -1.3122499645}
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