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Simplifying 20x3 + 85x2 = -60x Reorder the terms: 85x2 + 20x3 = -60x Solving 85x2 + 20x3 = -60x Solving for variable 'x'. Reorder the terms: 60x + 85x2 + 20x3 = -60x + 60x Combine like terms: -60x + 60x = 0 60x + 85x2 + 20x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(12 + 17x + 4x2) = 0 Ignore the factor 5.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 '(12 + 17x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + 17x + 4x2 = 0 Solving 12 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 4.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 4.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 4.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4.25x + x2 = 0 + -3 4.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4.25x + x2 = -3 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -3 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -3 + 4.515625 Combine like terms: -3 + 4.515625 = 1.515625 4.515625 + 4.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + 2.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + 2.125 = 1.231107225 Simplifying x + 2.125 = 1.231107225 Reorder the terms: 2.125 + x = 1.231107225 Solving 2.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.231107225 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.231107225 + -2.125 x = 1.231107225 + -2.125 Combine like terms: 1.231107225 + -2.125 = -0.893892775 x = -0.893892775 Simplifying x = -0.893892775Subproblem 2
x + 2.125 = -1.231107225 Simplifying x + 2.125 = -1.231107225 Reorder the terms: 2.125 + x = -1.231107225 Solving 2.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.231107225 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.231107225 + -2.125 x = -1.231107225 + -2.125 Combine like terms: -1.231107225 + -2.125 = -3.356107225 x = -3.356107225 Simplifying x = -3.356107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.893892775, -3.356107225}Solution
x = {0, -0.893892775, -3.356107225}
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