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Simplifying 10x3 + -120x2 + -168x = 0 Reorder the terms: -168x + -120x2 + 10x3 = 0 Solving -168x + -120x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-84 + -60x + 5x2) = 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 '(-84 + -60x + 5x2)' equal to zero and attempt to solve: Simplifying -84 + -60x + 5x2 = 0 Solving -84 + -60x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16.8 + -12x + x2 = 0 Move the constant term to the right: Add '16.8' to each side of the equation. -16.8 + -12x + 16.8 + x2 = 0 + 16.8 Reorder the terms: -16.8 + 16.8 + -12x + x2 = 0 + 16.8 Combine like terms: -16.8 + 16.8 = 0.0 0.0 + -12x + x2 = 0 + 16.8 -12x + x2 = 0 + 16.8 Combine like terms: 0 + 16.8 = 16.8 -12x + x2 = 16.8 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 16.8 + 36 Reorder the terms: 36 + -12x + x2 = 16.8 + 36 Combine like terms: 16.8 + 36 = 52.8 36 + -12x + x2 = 52.8 Factor a perfect square on the left side: (x + -6)(x + -6) = 52.8 Calculate the square root of the right side: 7.26636085 Break this problem into two subproblems by setting (x + -6) equal to 7.26636085 and -7.26636085.Subproblem 1
x + -6 = 7.26636085 Simplifying x + -6 = 7.26636085 Reorder the terms: -6 + x = 7.26636085 Solving -6 + x = 7.26636085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.26636085 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.26636085 + 6 x = 7.26636085 + 6 Combine like terms: 7.26636085 + 6 = 13.26636085 x = 13.26636085 Simplifying x = 13.26636085Subproblem 2
x + -6 = -7.26636085 Simplifying x + -6 = -7.26636085 Reorder the terms: -6 + x = -7.26636085 Solving -6 + x = -7.26636085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.26636085 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.26636085 + 6 x = -7.26636085 + 6 Combine like terms: -7.26636085 + 6 = -1.26636085 x = -1.26636085 Simplifying x = -1.26636085Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.26636085, -1.26636085}Solution
x = {0, 13.26636085, -1.26636085}
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