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Simplifying x2 + -9 + x(x + -1) = 180 Reorder the terms: x2 + -9 + x(-1 + x) = 180 x2 + -9 + (-1 * x + x * x) = 180 x2 + -9 + (-1x + x2) = 180 Reorder the terms: -9 + -1x + x2 + x2 = 180 Combine like terms: x2 + x2 = 2x2 -9 + -1x + 2x2 = 180 Solving -9 + -1x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -9 + -180 + -1x + 2x2 = 180 + -180 Combine like terms: -9 + -180 = -189 -189 + -1x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -189 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -94.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '94.5' to each side of the equation. -94.5 + -0.5x + 94.5 + x2 = 0 + 94.5 Reorder the terms: -94.5 + 94.5 + -0.5x + x2 = 0 + 94.5 Combine like terms: -94.5 + 94.5 = 0.0 0.0 + -0.5x + x2 = 0 + 94.5 -0.5x + x2 = 0 + 94.5 Combine like terms: 0 + 94.5 = 94.5 -0.5x + x2 = 94.5 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 = 94.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 94.5 + 0.0625 Combine like terms: 94.5 + 0.0625 = 94.5625 0.0625 + -0.5x + x2 = 94.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 94.5625 Calculate the square root of the right side: 9.724325169 Break this problem into two subproblems by setting (x + -0.25) equal to 9.724325169 and -9.724325169.Subproblem 1
x + -0.25 = 9.724325169 Simplifying x + -0.25 = 9.724325169 Reorder the terms: -0.25 + x = 9.724325169 Solving -0.25 + x = 9.724325169 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 = 9.724325169 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.724325169 + 0.25 x = 9.724325169 + 0.25 Combine like terms: 9.724325169 + 0.25 = 9.974325169 x = 9.974325169 Simplifying x = 9.974325169Subproblem 2
x + -0.25 = -9.724325169 Simplifying x + -0.25 = -9.724325169 Reorder the terms: -0.25 + x = -9.724325169 Solving -0.25 + x = -9.724325169 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 = -9.724325169 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.724325169 + 0.25 x = -9.724325169 + 0.25 Combine like terms: -9.724325169 + 0.25 = -9.474325169 x = -9.474325169 Simplifying x = -9.474325169Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.974325169, -9.474325169}
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