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Simplifying 12x3 = 60x2 + -70x Reorder the terms: 12x3 = -70x + 60x2 Solving 12x3 = -70x + 60x2 Solving for variable 'x'. Reorder the terms: 70x + -60x2 + 12x3 = -70x + 60x2 + 70x + -60x2 Reorder the terms: 70x + -60x2 + 12x3 = -70x + 70x + 60x2 + -60x2 Combine like terms: -70x + 70x = 0 70x + -60x2 + 12x3 = 0 + 60x2 + -60x2 70x + -60x2 + 12x3 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 70x + -60x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(35 + -30x + 6x2) = 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 '(35 + -30x + 6x2)' equal to zero and attempt to solve: Simplifying 35 + -30x + 6x2 = 0 Solving 35 + -30x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 5.833333333 + -5x + x2 = 0 Move the constant term to the right: Add '-5.833333333' to each side of the equation. 5.833333333 + -5x + -5.833333333 + x2 = 0 + -5.833333333 Reorder the terms: 5.833333333 + -5.833333333 + -5x + x2 = 0 + -5.833333333 Combine like terms: 5.833333333 + -5.833333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -5.833333333 -5x + x2 = 0 + -5.833333333 Combine like terms: 0 + -5.833333333 = -5.833333333 -5x + x2 = -5.833333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -5.833333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5.833333333 + 6.25 Combine like terms: -5.833333333 + 6.25 = 0.416666667 6.25 + -5x + x2 = 0.416666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.416666667 Calculate the square root of the right side: 0.645497225 Break this problem into two subproblems by setting (x + -2.5) equal to 0.645497225 and -0.645497225.Subproblem 1
x + -2.5 = 0.645497225 Simplifying x + -2.5 = 0.645497225 Reorder the terms: -2.5 + x = 0.645497225 Solving -2.5 + x = 0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 0.645497225 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.645497225 + 2.5 x = 0.645497225 + 2.5 Combine like terms: 0.645497225 + 2.5 = 3.145497225 x = 3.145497225 Simplifying x = 3.145497225Subproblem 2
x + -2.5 = -0.645497225 Simplifying x + -2.5 = -0.645497225 Reorder the terms: -2.5 + x = -0.645497225 Solving -2.5 + x = -0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -0.645497225 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.645497225 + 2.5 x = -0.645497225 + 2.5 Combine like terms: -0.645497225 + 2.5 = 1.854502775 x = 1.854502775 Simplifying x = 1.854502775Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.145497225, 1.854502775}Solution
x = {0, 3.145497225, 1.854502775}
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