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Simplifying 2x3 + -18x2 + -14x = 0 Reorder the terms: -14x + -18x2 + 2x3 = 0 Solving -14x + -18x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + -9x + x2) = 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 + -9x + x2)' equal to zero and attempt to solve: Simplifying -7 + -9x + x2 = 0 Solving -7 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -9x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -9x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9x + x2 = 0 + 7 -9x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9x + x2 = 7 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 7 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + -9x + x2 = 27.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -4.5 = 5.220153254 Simplifying x + -4.5 = 5.220153254 Reorder the terms: -4.5 + x = 5.220153254 Solving -4.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.220153254 + 4.5 x = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 x = 9.720153254 Simplifying x = 9.720153254Subproblem 2
x + -4.5 = -5.220153254 Simplifying x + -4.5 = -5.220153254 Reorder the terms: -4.5 + x = -5.220153254 Solving -4.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.220153254 + 4.5 x = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 x = -0.720153254 Simplifying x = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.720153254, -0.720153254}Solution
x = {0, 9.720153254, -0.720153254}
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