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Simplifying -1.25x2 + -450x + 72000 = 112500 Reorder the terms: 72000 + -450x + -1.25x2 = 112500 Solving 72000 + -450x + -1.25x2 = 112500 Solving for variable 'x'. Reorder the terms: 72000 + -112500 + -450x + -1.25x2 = 112500 + -112500 Combine like terms: 72000 + -112500 = -40500 -40500 + -450x + -1.25x2 = 112500 + -112500 Combine like terms: 112500 + -112500 = 0 -40500 + -450x + -1.25x2 = 0 Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. 32400 + 360x + x2 = 0 Move the constant term to the right: Add '-32400' to each side of the equation. 32400 + 360x + -32400 + x2 = 0 + -32400 Reorder the terms: 32400 + -32400 + 360x + x2 = 0 + -32400 Combine like terms: 32400 + -32400 = 0 0 + 360x + x2 = 0 + -32400 360x + x2 = 0 + -32400 Combine like terms: 0 + -32400 = -32400 360x + x2 = -32400 The x term is 360x. Take half its coefficient (180). Square it (32400) and add it to both sides. Add '32400' to each side of the equation. 360x + 32400 + x2 = -32400 + 32400 Reorder the terms: 32400 + 360x + x2 = -32400 + 32400 Combine like terms: -32400 + 32400 = 0 32400 + 360x + x2 = 0 Factor a perfect square on the left side: (x + 180)(x + 180) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + 180) equal to 0 and 0.Subproblem 1
x + 180 = 0 Simplifying x + 180 = 0 Reorder the terms: 180 + x = 0 Solving 180 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + x = 0 + -180 Combine like terms: 180 + -180 = 0 0 + x = 0 + -180 x = 0 + -180 Combine like terms: 0 + -180 = -180 x = -180 Simplifying x = -180Subproblem 2
x + 180 = 0 Simplifying x + 180 = 0 Reorder the terms: 180 + x = 0 Solving 180 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + x = 0 + -180 Combine like terms: 180 + -180 = 0 0 + x = 0 + -180 x = 0 + -180 Combine like terms: 0 + -180 = -180 x = -180 Simplifying x = -180Solution
The solution to the problem is based on the solutions from the subproblems. x = {-180, -180}
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