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Simplifying -0.2x2 + 115x + -7200 = 0 Reorder the terms: -7200 + 115x + -0.2x2 = 0 Solving -7200 + 115x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 36000 + -575x + x2 = 0 Move the constant term to the right: Add '-36000' to each side of the equation. 36000 + -575x + -36000 + x2 = 0 + -36000 Reorder the terms: 36000 + -36000 + -575x + x2 = 0 + -36000 Combine like terms: 36000 + -36000 = 0 0 + -575x + x2 = 0 + -36000 -575x + x2 = 0 + -36000 Combine like terms: 0 + -36000 = -36000 -575x + x2 = -36000 The x term is -575x. Take half its coefficient (-287.5). Square it (82656.25) and add it to both sides. Add '82656.25' to each side of the equation. -575x + 82656.25 + x2 = -36000 + 82656.25 Reorder the terms: 82656.25 + -575x + x2 = -36000 + 82656.25 Combine like terms: -36000 + 82656.25 = 46656.25 82656.25 + -575x + x2 = 46656.25 Factor a perfect square on the left side: (x + -287.5)(x + -287.5) = 46656.25 Calculate the square root of the right side: 216.000578703 Break this problem into two subproblems by setting (x + -287.5) equal to 216.000578703 and -216.000578703.Subproblem 1
x + -287.5 = 216.000578703 Simplifying x + -287.5 = 216.000578703 Reorder the terms: -287.5 + x = 216.000578703 Solving -287.5 + x = 216.000578703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '287.5' to each side of the equation. -287.5 + 287.5 + x = 216.000578703 + 287.5 Combine like terms: -287.5 + 287.5 = 0.0 0.0 + x = 216.000578703 + 287.5 x = 216.000578703 + 287.5 Combine like terms: 216.000578703 + 287.5 = 503.500578703 x = 503.500578703 Simplifying x = 503.500578703Subproblem 2
x + -287.5 = -216.000578703 Simplifying x + -287.5 = -216.000578703 Reorder the terms: -287.5 + x = -216.000578703 Solving -287.5 + x = -216.000578703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '287.5' to each side of the equation. -287.5 + 287.5 + x = -216.000578703 + 287.5 Combine like terms: -287.5 + 287.5 = 0.0 0.0 + x = -216.000578703 + 287.5 x = -216.000578703 + 287.5 Combine like terms: -216.000578703 + 287.5 = 71.499421297 x = 71.499421297 Simplifying x = 71.499421297Solution
The solution to the problem is based on the solutions from the subproblems. x = {503.500578703, 71.499421297}
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