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Simplifying (x2 + -15) + x(x + -1) = 180 Reorder the terms: (-15 + x2) + x(x + -1) = 180 Remove parenthesis around (-15 + x2) -15 + x2 + x(x + -1) = 180 Reorder the terms: -15 + x2 + x(-1 + x) = 180 -15 + x2 + (-1 * x + x * x) = 180 -15 + x2 + (-1x + x2) = 180 Reorder the terms: -15 + -1x + x2 + x2 = 180 Combine like terms: x2 + x2 = 2x2 -15 + -1x + 2x2 = 180 Solving -15 + -1x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -15 + -180 + -1x + 2x2 = 180 + -180 Combine like terms: -15 + -180 = -195 -195 + -1x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -195 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -97.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '97.5' to each side of the equation. -97.5 + -0.5x + 97.5 + x2 = 0 + 97.5 Reorder the terms: -97.5 + 97.5 + -0.5x + x2 = 0 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + -0.5x + x2 = 0 + 97.5 -0.5x + x2 = 0 + 97.5 Combine like terms: 0 + 97.5 = 97.5 -0.5x + x2 = 97.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 97.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 97.5 + 0.0625 Combine like terms: 97.5 + 0.0625 = 97.5625 0.0625 + -0.5x + x2 = 97.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 97.5625 Calculate the square root of the right side: 9.877373133 Break this problem into two subproblems by setting (x + -0.25) equal to 9.877373133 and -9.877373133.Subproblem 1
x + -0.25 = 9.877373133 Simplifying x + -0.25 = 9.877373133 Reorder the terms: -0.25 + x = 9.877373133 Solving -0.25 + x = 9.877373133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 9.877373133 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.877373133 + 0.25 x = 9.877373133 + 0.25 Combine like terms: 9.877373133 + 0.25 = 10.127373133 x = 10.127373133 Simplifying x = 10.127373133Subproblem 2
x + -0.25 = -9.877373133 Simplifying x + -0.25 = -9.877373133 Reorder the terms: -0.25 + x = -9.877373133 Solving -0.25 + x = -9.877373133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -9.877373133 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.877373133 + 0.25 x = -9.877373133 + 0.25 Combine like terms: -9.877373133 + 0.25 = -9.627373133 x = -9.627373133 Simplifying x = -9.627373133Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.127373133, -9.627373133}
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