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Simplifying -0.5x2 + 270x + -33637.5 = 0 Reorder the terms: -33637.5 + 270x + -0.5x2 = 0 Solving -33637.5 + 270x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 67275 + -540x + x2 = 0 Move the constant term to the right: Add '-67275' to each side of the equation. 67275 + -540x + -67275 + x2 = 0 + -67275 Reorder the terms: 67275 + -67275 + -540x + x2 = 0 + -67275 Combine like terms: 67275 + -67275 = 0 0 + -540x + x2 = 0 + -67275 -540x + x2 = 0 + -67275 Combine like terms: 0 + -67275 = -67275 -540x + x2 = -67275 The x term is -540x. Take half its coefficient (-270). Square it (72900) and add it to both sides. Add '72900' to each side of the equation. -540x + 72900 + x2 = -67275 + 72900 Reorder the terms: 72900 + -540x + x2 = -67275 + 72900 Combine like terms: -67275 + 72900 = 5625 72900 + -540x + x2 = 5625 Factor a perfect square on the left side: (x + -270)(x + -270) = 5625 Calculate the square root of the right side: 75 Break this problem into two subproblems by setting (x + -270) equal to 75 and -75.Subproblem 1
x + -270 = 75 Simplifying x + -270 = 75 Reorder the terms: -270 + x = 75 Solving -270 + x = 75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '270' to each side of the equation. -270 + 270 + x = 75 + 270 Combine like terms: -270 + 270 = 0 0 + x = 75 + 270 x = 75 + 270 Combine like terms: 75 + 270 = 345 x = 345 Simplifying x = 345Subproblem 2
x + -270 = -75 Simplifying x + -270 = -75 Reorder the terms: -270 + x = -75 Solving -270 + x = -75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '270' to each side of the equation. -270 + 270 + x = -75 + 270 Combine like terms: -270 + 270 = 0 0 + x = -75 + 270 x = -75 + 270 Combine like terms: -75 + 270 = 195 x = 195 Simplifying x = 195Solution
The solution to the problem is based on the solutions from the subproblems. x = {345, 195}
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