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Simplifying 3x3 + -45x2 = 62x Reorder the terms: -45x2 + 3x3 = 62x Solving -45x2 + 3x3 = 62x Solving for variable 'x'. Reorder the terms: -62x + -45x2 + 3x3 = 62x + -62x Combine like terms: 62x + -62x = 0 -62x + -45x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-62 + -45x + 3x2) = 0Subproblem 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 '(-62 + -45x + 3x2)' equal to zero and attempt to solve: Simplifying -62 + -45x + 3x2 = 0 Solving -62 + -45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20.66666667 + -15x + x2 = 0 Move the constant term to the right: Add '20.66666667' to each side of the equation. -20.66666667 + -15x + 20.66666667 + x2 = 0 + 20.66666667 Reorder the terms: -20.66666667 + 20.66666667 + -15x + x2 = 0 + 20.66666667 Combine like terms: -20.66666667 + 20.66666667 = 0.00000000 0.00000000 + -15x + x2 = 0 + 20.66666667 -15x + x2 = 0 + 20.66666667 Combine like terms: 0 + 20.66666667 = 20.66666667 -15x + x2 = 20.66666667 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 20.66666667 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 20.66666667 + 56.25 Combine like terms: 20.66666667 + 56.25 = 76.91666667 56.25 + -15x + x2 = 76.91666667 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 76.91666667 Calculate the square root of the right side: 8.770214745 Break this problem into two subproblems by setting (x + -7.5) equal to 8.770214745 and -8.770214745.Subproblem 1
x + -7.5 = 8.770214745 Simplifying x + -7.5 = 8.770214745 Reorder the terms: -7.5 + x = 8.770214745 Solving -7.5 + x = 8.770214745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.770214745 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.770214745 + 7.5 x = 8.770214745 + 7.5 Combine like terms: 8.770214745 + 7.5 = 16.270214745 x = 16.270214745 Simplifying x = 16.270214745Subproblem 2
x + -7.5 = -8.770214745 Simplifying x + -7.5 = -8.770214745 Reorder the terms: -7.5 + x = -8.770214745 Solving -7.5 + x = -8.770214745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.770214745 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.770214745 + 7.5 x = -8.770214745 + 7.5 Combine like terms: -8.770214745 + 7.5 = -1.270214745 x = -1.270214745 Simplifying x = -1.270214745Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.270214745, -1.270214745}Solution
x = {0, 16.270214745, -1.270214745}
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