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Simplifying x2 + 150x + -39375 = 0 Reorder the terms: -39375 + 150x + x2 = 0 Solving -39375 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39375' to each side of the equation. -39375 + 150x + 39375 + x2 = 0 + 39375 Reorder the terms: -39375 + 39375 + 150x + x2 = 0 + 39375 Combine like terms: -39375 + 39375 = 0 0 + 150x + x2 = 0 + 39375 150x + x2 = 0 + 39375 Combine like terms: 0 + 39375 = 39375 150x + x2 = 39375 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 = 39375 + 5625 Reorder the terms: 5625 + 150x + x2 = 39375 + 5625 Combine like terms: 39375 + 5625 = 45000 5625 + 150x + x2 = 45000 Factor a perfect square on the left side: (x + 75)(x + 75) = 45000 Calculate the square root of the right side: 212.132034356 Break this problem into two subproblems by setting (x + 75) equal to 212.132034356 and -212.132034356.Subproblem 1
x + 75 = 212.132034356 Simplifying x + 75 = 212.132034356 Reorder the terms: 75 + x = 212.132034356 Solving 75 + x = 212.132034356 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 = 212.132034356 + -75 Combine like terms: 75 + -75 = 0 0 + x = 212.132034356 + -75 x = 212.132034356 + -75 Combine like terms: 212.132034356 + -75 = 137.132034356 x = 137.132034356 Simplifying x = 137.132034356Subproblem 2
x + 75 = -212.132034356 Simplifying x + 75 = -212.132034356 Reorder the terms: 75 + x = -212.132034356 Solving 75 + x = -212.132034356 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 = -212.132034356 + -75 Combine like terms: 75 + -75 = 0 0 + x = -212.132034356 + -75 x = -212.132034356 + -75 Combine like terms: -212.132034356 + -75 = -287.132034356 x = -287.132034356 Simplifying x = -287.132034356Solution
The solution to the problem is based on the solutions from the subproblems. x = {137.132034356, -287.132034356}
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