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Simplifying x2 + -117x + -180 = 0 Reorder the terms: -180 + -117x + x2 = 0 Solving -180 + -117x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -117x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -117x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -117x + x2 = 0 + 180 -117x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -117x + x2 = 180 The x term is -117x. Take half its coefficient (-58.5). Square it (3422.25) and add it to both sides. Add '3422.25' to each side of the equation. -117x + 3422.25 + x2 = 180 + 3422.25 Reorder the terms: 3422.25 + -117x + x2 = 180 + 3422.25 Combine like terms: 180 + 3422.25 = 3602.25 3422.25 + -117x + x2 = 3602.25 Factor a perfect square on the left side: (x + -58.5)(x + -58.5) = 3602.25 Calculate the square root of the right side: 60.018747071 Break this problem into two subproblems by setting (x + -58.5) equal to 60.018747071 and -60.018747071.Subproblem 1
x + -58.5 = 60.018747071 Simplifying x + -58.5 = 60.018747071 Reorder the terms: -58.5 + x = 60.018747071 Solving -58.5 + x = 60.018747071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = 60.018747071 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = 60.018747071 + 58.5 x = 60.018747071 + 58.5 Combine like terms: 60.018747071 + 58.5 = 118.518747071 x = 118.518747071 Simplifying x = 118.518747071Subproblem 2
x + -58.5 = -60.018747071 Simplifying x + -58.5 = -60.018747071 Reorder the terms: -58.5 + x = -60.018747071 Solving -58.5 + x = -60.018747071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = -60.018747071 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = -60.018747071 + 58.5 x = -60.018747071 + 58.5 Combine like terms: -60.018747071 + 58.5 = -1.518747071 x = -1.518747071 Simplifying x = -1.518747071Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.518747071, -1.518747071}
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