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Simplifying 0 = 2x3 + -80x2 + 75x Reorder the terms: 0 = 75x + -80x2 + 2x3 Solving 0 = 75x + -80x2 + 2x3 Solving for variable 'x'. Remove the zero: -75x + 80x2 + -2x3 = 75x + -80x2 + 2x3 + -75x + 80x2 + -2x3 Reorder the terms: -75x + 80x2 + -2x3 = 75x + -75x + -80x2 + 80x2 + 2x3 + -2x3 Combine like terms: 75x + -75x = 0 -75x + 80x2 + -2x3 = 0 + -80x2 + 80x2 + 2x3 + -2x3 -75x + 80x2 + -2x3 = -80x2 + 80x2 + 2x3 + -2x3 Combine like terms: -80x2 + 80x2 = 0 -75x + 80x2 + -2x3 = 0 + 2x3 + -2x3 -75x + 80x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -75x + 80x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-75 + 80x + -2x2) = 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 '(-75 + 80x + -2x2)' equal to zero and attempt to solve: Simplifying -75 + 80x + -2x2 = 0 Solving -75 + 80x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 37.5 + -40x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -40x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -40x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -40x + x2 = 0 + -37.5 -40x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -40x + x2 = -37.5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -37.5 + 400 Reorder the terms: 400 + -40x + x2 = -37.5 + 400 Combine like terms: -37.5 + 400 = 362.5 400 + -40x + x2 = 362.5 Factor a perfect square on the left side: (x + -20)(x + -20) = 362.5 Calculate the square root of the right side: 19.039432765 Break this problem into two subproblems by setting (x + -20) equal to 19.039432765 and -19.039432765.Subproblem 1
x + -20 = 19.039432765 Simplifying x + -20 = 19.039432765 Reorder the terms: -20 + x = 19.039432765 Solving -20 + x = 19.039432765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.039432765 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.039432765 + 20 x = 19.039432765 + 20 Combine like terms: 19.039432765 + 20 = 39.039432765 x = 39.039432765 Simplifying x = 39.039432765Subproblem 2
x + -20 = -19.039432765 Simplifying x + -20 = -19.039432765 Reorder the terms: -20 + x = -19.039432765 Solving -20 + x = -19.039432765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.039432765 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.039432765 + 20 x = -19.039432765 + 20 Combine like terms: -19.039432765 + 20 = 0.960567235 x = 0.960567235 Simplifying x = 0.960567235Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.039432765, 0.960567235}Solution
x = {0, 39.039432765, 0.960567235}
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