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Simplifying -15x2 + 225x + -180 = 0 Reorder the terms: -180 + 225x + -15x2 = 0 Solving -180 + 225x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(-12 + 15x + -1x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-12 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying -12 + 15x + -1x2 = 0 Solving -12 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -15x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -15x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -15x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -15x + x2 = 0 + -12 -15x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -15x + x2 = -12 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 = -12 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -12 + 56.25 Combine like terms: -12 + 56.25 = 44.25 56.25 + -15x + x2 = 44.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -7.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -7.5 = 6.652067348 Simplifying x + -7.5 = 6.652067348 Reorder the terms: -7.5 + x = 6.652067348 Solving -7.5 + x = 6.652067348 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 = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.652067348 + 7.5 x = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 x = 14.152067348 Simplifying x = 14.152067348Subproblem 2
x + -7.5 = -6.652067348 Simplifying x + -7.5 = -6.652067348 Reorder the terms: -7.5 + x = -6.652067348 Solving -7.5 + x = -6.652067348 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 = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.652067348 + 7.5 x = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 x = 0.847932652 Simplifying x = 0.847932652Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.152067348, 0.847932652}Solution
x = {14.152067348, 0.847932652}
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