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Simplifying 0 = -12x3 + 84x2 + -60x Reorder the terms: 0 = -60x + 84x2 + -12x3 Solving 0 = -60x + 84x2 + -12x3 Solving for variable 'x'. Remove the zero: 60x + -84x2 + 12x3 = -60x + 84x2 + -12x3 + 60x + -84x2 + 12x3 Reorder the terms: 60x + -84x2 + 12x3 = -60x + 60x + 84x2 + -84x2 + -12x3 + 12x3 Combine like terms: -60x + 60x = 0 60x + -84x2 + 12x3 = 0 + 84x2 + -84x2 + -12x3 + 12x3 60x + -84x2 + 12x3 = 84x2 + -84x2 + -12x3 + 12x3 Combine like terms: 84x2 + -84x2 = 0 60x + -84x2 + 12x3 = 0 + -12x3 + 12x3 60x + -84x2 + 12x3 = -12x3 + 12x3 Combine like terms: -12x3 + 12x3 = 0 60x + -84x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '12x'. 12x(5 + -7x + x2) = 0 Ignore the factor 12.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 + -7x + x2)' equal to zero and attempt to solve: Simplifying 5 + -7x + x2 = 0 Solving 5 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x + x2 = 0 + -5 -7x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7x + x2 = -5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -5 + 12.25 Combine like terms: -5 + 12.25 = 7.25 12.25 + -7x + x2 = 7.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -3.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -3.5 = 2.692582404 Simplifying x + -3.5 = 2.692582404 Reorder the terms: -3.5 + x = 2.692582404 Solving -3.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.692582404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.692582404 + 3.5 x = 2.692582404 + 3.5 Combine like terms: 2.692582404 + 3.5 = 6.192582404 x = 6.192582404 Simplifying x = 6.192582404Subproblem 2
x + -3.5 = -2.692582404 Simplifying x + -3.5 = -2.692582404 Reorder the terms: -3.5 + x = -2.692582404 Solving -3.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.692582404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.692582404 + 3.5 x = -2.692582404 + 3.5 Combine like terms: -2.692582404 + 3.5 = 0.807417596 x = 0.807417596 Simplifying x = 0.807417596Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.192582404, 0.807417596}Solution
x = {0, 6.192582404, 0.807417596}
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