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Simplifying (5x3 + x2 + -9x)(8xy) = 0 Reorder the terms: (-9x + x2 + 5x3)(8xy) = 0 Remove parenthesis around (8xy) (-9x + x2 + 5x3) * 8xy = 0 Reorder the terms for easier multiplication: 8xy(-9x + x2 + 5x3) = 0 (-9x * 8xy + x2 * 8xy + 5x3 * 8xy) = 0 (-72x2y + 8x3y + 40x4y) = 0 Solving -72x2y + 8x3y + 40x4y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x2y'. 8x2y(-9 + x + 5x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve: Simplifying x2y = 0 Solving x2y = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2y = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9 + x + 5x2)' equal to zero and attempt to solve: Simplifying -9 + x + 5x2 = 0 Solving -9 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.2x + x2 = 0 + 1.8 0.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.2x + x2 = 1.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2x + 0.25 + x2 = 1.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 1.8 + 0.25 Combine like terms: 1.8 + 0.25 = 2.05 0.25 + 0.2x + x2 = 2.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.05 Calculate the square root of the right side: 1.431782106 Break this problem into two subproblems by setting (x + 0.5) equal to 1.431782106 and -1.431782106.Subproblem 1
x + 0.5 = 1.431782106 Simplifying x + 0.5 = 1.431782106 Reorder the terms: 0.5 + x = 1.431782106 Solving 0.5 + x = 1.431782106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.431782106 + -0.5 x = 1.431782106 + -0.5 Combine like terms: 1.431782106 + -0.5 = 0.931782106 x = 0.931782106 Simplifying x = 0.931782106Subproblem 2
x + 0.5 = -1.431782106 Simplifying x + 0.5 = -1.431782106 Reorder the terms: 0.5 + x = -1.431782106 Solving 0.5 + x = -1.431782106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.431782106 + -0.5 x = -1.431782106 + -0.5 Combine like terms: -1.431782106 + -0.5 = -1.931782106 x = -1.931782106 Simplifying x = -1.931782106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.931782106, -1.931782106}Solution
x = {0.931782106, -1.931782106}
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