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Simplifying 18x3 + -34x2 + -16x = 0 Reorder the terms: -16x + -34x2 + 18x3 = 0 Solving -16x + -34x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + -17x + 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 '(-8 + -17x + 9x2)' equal to zero and attempt to solve: Simplifying -8 + -17x + 9x2 = 0 Solving -8 + -17x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -1.888888889x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -1.888888889x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + 0.8888888889 -1.888888889x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -1.888888889x + x2 = 0.8888888889 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 0.8888888889 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 0.8888888889 + 0.8919753087 Combine like terms: 0.8888888889 + 0.8919753087 = 1.7808641976 0.8919753087 + -1.888888889x + x2 = 1.7808641976 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 1.7808641976 Calculate the square root of the right side: 1.334490239 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.334490239 and -1.334490239.Subproblem 1
x + -0.9444444445 = 1.334490239 Simplifying x + -0.9444444445 = 1.334490239 Reorder the terms: -0.9444444445 + x = 1.334490239 Solving -0.9444444445 + x = 1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.334490239 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.334490239 + 0.9444444445 x = 1.334490239 + 0.9444444445 Combine like terms: 1.334490239 + 0.9444444445 = 2.2789346835 x = 2.2789346835 Simplifying x = 2.2789346835Subproblem 2
x + -0.9444444445 = -1.334490239 Simplifying x + -0.9444444445 = -1.334490239 Reorder the terms: -0.9444444445 + x = -1.334490239 Solving -0.9444444445 + x = -1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.334490239 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.334490239 + 0.9444444445 x = -1.334490239 + 0.9444444445 Combine like terms: -1.334490239 + 0.9444444445 = -0.3900457945 x = -0.3900457945 Simplifying x = -0.3900457945Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2789346835, -0.3900457945}Solution
x = {0, 2.2789346835, -0.3900457945}
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