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Simplifying 2x2 + -115x + 180 = 0 Reorder the terms: 180 + -115x + 2x2 = 0 Solving 180 + -115x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 90 + -57.5x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -57.5x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -57.5x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -57.5x + x2 = 0 + -90 -57.5x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -57.5x + x2 = -90 The x term is -57.5x. Take half its coefficient (-28.75). Square it (826.5625) and add it to both sides. Add '826.5625' to each side of the equation. -57.5x + 826.5625 + x2 = -90 + 826.5625 Reorder the terms: 826.5625 + -57.5x + x2 = -90 + 826.5625 Combine like terms: -90 + 826.5625 = 736.5625 826.5625 + -57.5x + x2 = 736.5625 Factor a perfect square on the left side: (x + -28.75)(x + -28.75) = 736.5625 Calculate the square root of the right side: 27.139684965 Break this problem into two subproblems by setting (x + -28.75) equal to 27.139684965 and -27.139684965.Subproblem 1
x + -28.75 = 27.139684965 Simplifying x + -28.75 = 27.139684965 Reorder the terms: -28.75 + x = 27.139684965 Solving -28.75 + x = 27.139684965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.75' to each side of the equation. -28.75 + 28.75 + x = 27.139684965 + 28.75 Combine like terms: -28.75 + 28.75 = 0.00 0.00 + x = 27.139684965 + 28.75 x = 27.139684965 + 28.75 Combine like terms: 27.139684965 + 28.75 = 55.889684965 x = 55.889684965 Simplifying x = 55.889684965Subproblem 2
x + -28.75 = -27.139684965 Simplifying x + -28.75 = -27.139684965 Reorder the terms: -28.75 + x = -27.139684965 Solving -28.75 + x = -27.139684965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.75' to each side of the equation. -28.75 + 28.75 + x = -27.139684965 + 28.75 Combine like terms: -28.75 + 28.75 = 0.00 0.00 + x = -27.139684965 + 28.75 x = -27.139684965 + 28.75 Combine like terms: -27.139684965 + 28.75 = 1.610315035 x = 1.610315035 Simplifying x = 1.610315035Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.889684965, 1.610315035}
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