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Simplifying 15x3 + -21x2 + -560x = 0 Reorder the terms: -560x + -21x2 + 15x3 = 0 Solving -560x + -21x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-560 + -21x + 15x2) = 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 '(-560 + -21x + 15x2)' equal to zero and attempt to solve: Simplifying -560 + -21x + 15x2 = 0 Solving -560 + -21x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -37.33333333 + -1.4x + x2 = 0 Move the constant term to the right: Add '37.33333333' to each side of the equation. -37.33333333 + -1.4x + 37.33333333 + x2 = 0 + 37.33333333 Reorder the terms: -37.33333333 + 37.33333333 + -1.4x + x2 = 0 + 37.33333333 Combine like terms: -37.33333333 + 37.33333333 = 0.00000000 0.00000000 + -1.4x + x2 = 0 + 37.33333333 -1.4x + x2 = 0 + 37.33333333 Combine like terms: 0 + 37.33333333 = 37.33333333 -1.4x + x2 = 37.33333333 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 37.33333333 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 37.33333333 + 0.49 Combine like terms: 37.33333333 + 0.49 = 37.82333333 0.49 + -1.4x + x2 = 37.82333333 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 37.82333333 Calculate the square root of the right side: 6.15006775 Break this problem into two subproblems by setting (x + -0.7) equal to 6.15006775 and -6.15006775.Subproblem 1
x + -0.7 = 6.15006775 Simplifying x + -0.7 = 6.15006775 Reorder the terms: -0.7 + x = 6.15006775 Solving -0.7 + x = 6.15006775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 6.15006775 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 6.15006775 + 0.7 x = 6.15006775 + 0.7 Combine like terms: 6.15006775 + 0.7 = 6.85006775 x = 6.85006775 Simplifying x = 6.85006775Subproblem 2
x + -0.7 = -6.15006775 Simplifying x + -0.7 = -6.15006775 Reorder the terms: -0.7 + x = -6.15006775 Solving -0.7 + x = -6.15006775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -6.15006775 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -6.15006775 + 0.7 x = -6.15006775 + 0.7 Combine like terms: -6.15006775 + 0.7 = -5.45006775 x = -5.45006775 Simplifying x = -5.45006775Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.85006775, -5.45006775}Solution
x = {0, 6.85006775, -5.45006775}
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