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Simplifying x2 + 150x + 500 = 15000 Reorder the terms: 500 + 150x + x2 = 15000 Solving 500 + 150x + x2 = 15000 Solving for variable 'x'. Reorder the terms: 500 + -15000 + 150x + x2 = 15000 + -15000 Combine like terms: 500 + -15000 = -14500 -14500 + 150x + x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 -14500 + 150x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14500' to each side of the equation. -14500 + 150x + 14500 + x2 = 0 + 14500 Reorder the terms: -14500 + 14500 + 150x + x2 = 0 + 14500 Combine like terms: -14500 + 14500 = 0 0 + 150x + x2 = 0 + 14500 150x + x2 = 0 + 14500 Combine like terms: 0 + 14500 = 14500 150x + x2 = 14500 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 = 14500 + 5625 Reorder the terms: 5625 + 150x + x2 = 14500 + 5625 Combine like terms: 14500 + 5625 = 20125 5625 + 150x + x2 = 20125 Factor a perfect square on the left side: (x + 75)(x + 75) = 20125 Calculate the square root of the right side: 141.862609591 Break this problem into two subproblems by setting (x + 75) equal to 141.862609591 and -141.862609591.Subproblem 1
x + 75 = 141.862609591 Simplifying x + 75 = 141.862609591 Reorder the terms: 75 + x = 141.862609591 Solving 75 + x = 141.862609591 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 = 141.862609591 + -75 Combine like terms: 75 + -75 = 0 0 + x = 141.862609591 + -75 x = 141.862609591 + -75 Combine like terms: 141.862609591 + -75 = 66.862609591 x = 66.862609591 Simplifying x = 66.862609591Subproblem 2
x + 75 = -141.862609591 Simplifying x + 75 = -141.862609591 Reorder the terms: 75 + x = -141.862609591 Solving 75 + x = -141.862609591 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 = -141.862609591 + -75 Combine like terms: 75 + -75 = 0 0 + x = -141.862609591 + -75 x = -141.862609591 + -75 Combine like terms: -141.862609591 + -75 = -216.862609591 x = -216.862609591 Simplifying x = -216.862609591Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.862609591, -216.862609591}
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