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Simplifying x2 = 15x + 180 Reorder the terms: x2 = 180 + 15x Solving x2 = 180 + 15x Solving for variable 'x'. Reorder the terms: -180 + -15x + x2 = 180 + 15x + -180 + -15x Reorder the terms: -180 + -15x + x2 = 180 + -180 + 15x + -15x Combine like terms: 180 + -180 = 0 -180 + -15x + x2 = 0 + 15x + -15x -180 + -15x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -180 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -15x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -15x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -15x + x2 = 0 + 180 -15x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -15x + x2 = 180 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 = 180 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 180 + 56.25 Combine like terms: 180 + 56.25 = 236.25 56.25 + -15x + x2 = 236.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + -7.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + -7.5 = 15.370426149 Simplifying x + -7.5 = 15.370426149 Reorder the terms: -7.5 + x = 15.370426149 Solving -7.5 + x = 15.370426149 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 = 15.370426149 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 15.370426149 + 7.5 x = 15.370426149 + 7.5 Combine like terms: 15.370426149 + 7.5 = 22.870426149 x = 22.870426149 Simplifying x = 22.870426149Subproblem 2
x + -7.5 = -15.370426149 Simplifying x + -7.5 = -15.370426149 Reorder the terms: -7.5 + x = -15.370426149 Solving -7.5 + x = -15.370426149 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 = -15.370426149 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -15.370426149 + 7.5 x = -15.370426149 + 7.5 Combine like terms: -15.370426149 + 7.5 = -7.870426149 x = -7.870426149 Simplifying x = -7.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.870426149, -7.870426149}
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