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Simplifying 9x(x + -15) = 45 Reorder the terms: 9x(-15 + x) = 45 (-15 * 9x + x * 9x) = 45 (-135x + 9x2) = 45 Solving -135x + 9x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -135x + 9x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -135x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-5 + -15x + x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-5 + -15x + x2)' equal to zero and attempt to solve: Simplifying -5 + -15x + x2 = 0 Solving -5 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -15x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -15x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -15x + x2 = 0 + 5 -15x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -15x + x2 = 5 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 = 5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 5 + 56.25 Combine like terms: 5 + 56.25 = 61.25 56.25 + -15x + x2 = 61.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + -7.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + -7.5 = 7.826237921 Simplifying x + -7.5 = 7.826237921 Reorder the terms: -7.5 + x = 7.826237921 Solving -7.5 + x = 7.826237921 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 = 7.826237921 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.826237921 + 7.5 x = 7.826237921 + 7.5 Combine like terms: 7.826237921 + 7.5 = 15.326237921 x = 15.326237921 Simplifying x = 15.326237921Subproblem 2
x + -7.5 = -7.826237921 Simplifying x + -7.5 = -7.826237921 Reorder the terms: -7.5 + x = -7.826237921 Solving -7.5 + x = -7.826237921 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 = -7.826237921 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.826237921 + 7.5 x = -7.826237921 + 7.5 Combine like terms: -7.826237921 + 7.5 = -0.326237921 x = -0.326237921 Simplifying x = -0.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.326237921, -0.326237921}Solution
x = {15.326237921, -0.326237921}
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