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Simplifying -1x2 + 150x + -2500 = 0 Reorder the terms: -2500 + 150x + -1x2 = 0 Solving -2500 + 150x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2500 + -150x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -150x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -150x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -150x + x2 = 0 + -2500 -150x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -150x + x2 = -2500 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -2500 + 5625 Reorder the terms: 5625 + -150x + x2 = -2500 + 5625 Combine like terms: -2500 + 5625 = 3125 5625 + -150x + x2 = 3125 Factor a perfect square on the left side: (x + -75)(x + -75) = 3125 Calculate the square root of the right side: 55.901699437 Break this problem into two subproblems by setting (x + -75) equal to 55.901699437 and -55.901699437.Subproblem 1
x + -75 = 55.901699437 Simplifying x + -75 = 55.901699437 Reorder the terms: -75 + x = 55.901699437 Solving -75 + x = 55.901699437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 55.901699437 + 75 Combine like terms: -75 + 75 = 0 0 + x = 55.901699437 + 75 x = 55.901699437 + 75 Combine like terms: 55.901699437 + 75 = 130.901699437 x = 130.901699437 Simplifying x = 130.901699437Subproblem 2
x + -75 = -55.901699437 Simplifying x + -75 = -55.901699437 Reorder the terms: -75 + x = -55.901699437 Solving -75 + x = -55.901699437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -55.901699437 + 75 Combine like terms: -75 + 75 = 0 0 + x = -55.901699437 + 75 x = -55.901699437 + 75 Combine like terms: -55.901699437 + 75 = 19.098300563 x = 19.098300563 Simplifying x = 19.098300563Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.901699437, 19.098300563}
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