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Simplifying 4x3 + -34x2 + -30x = 0 Reorder the terms: -30x + -34x2 + 4x3 = 0 Solving -30x + -34x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-15 + -17x + 2x2) = 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 '(-15 + -17x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + -17x + 2x2 = 0 Solving -15 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -8.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -8.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -8.5x + x2 = 0 + 7.5 -8.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -8.5x + x2 = 7.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 7.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 7.5 + 18.0625 Combine like terms: 7.5 + 18.0625 = 25.5625 18.0625 + -8.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -4.25) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -4.25 = 5.055937104 Simplifying x + -4.25 = 5.055937104 Reorder the terms: -4.25 + x = 5.055937104 Solving -4.25 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 5.055937104 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 5.055937104 + 4.25 x = 5.055937104 + 4.25 Combine like terms: 5.055937104 + 4.25 = 9.305937104 x = 9.305937104 Simplifying x = 9.305937104Subproblem 2
x + -4.25 = -5.055937104 Simplifying x + -4.25 = -5.055937104 Reorder the terms: -4.25 + x = -5.055937104 Solving -4.25 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -5.055937104 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -5.055937104 + 4.25 x = -5.055937104 + 4.25 Combine like terms: -5.055937104 + 4.25 = -0.805937104 x = -0.805937104 Simplifying x = -0.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.305937104, -0.805937104}Solution
x = {0, 9.305937104, -0.805937104}
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