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Simplifying x2 + 300x + 17500 = 0 Reorder the terms: 17500 + 300x + x2 = 0 Solving 17500 + 300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17500' to each side of the equation. 17500 + 300x + -17500 + x2 = 0 + -17500 Reorder the terms: 17500 + -17500 + 300x + x2 = 0 + -17500 Combine like terms: 17500 + -17500 = 0 0 + 300x + x2 = 0 + -17500 300x + x2 = 0 + -17500 Combine like terms: 0 + -17500 = -17500 300x + x2 = -17500 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = -17500 + 22500 Reorder the terms: 22500 + 300x + x2 = -17500 + 22500 Combine like terms: -17500 + 22500 = 5000 22500 + 300x + x2 = 5000 Factor a perfect square on the left side: (x + 150)(x + 150) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + 150) equal to 70.710678119 and -70.710678119.Subproblem 1
x + 150 = 70.710678119 Simplifying x + 150 = 70.710678119 Reorder the terms: 150 + x = 70.710678119 Solving 150 + x = 70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 70.710678119 + -150 Combine like terms: 150 + -150 = 0 0 + x = 70.710678119 + -150 x = 70.710678119 + -150 Combine like terms: 70.710678119 + -150 = -79.289321881 x = -79.289321881 Simplifying x = -79.289321881Subproblem 2
x + 150 = -70.710678119 Simplifying x + 150 = -70.710678119 Reorder the terms: 150 + x = -70.710678119 Solving 150 + x = -70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -70.710678119 + -150 Combine like terms: 150 + -150 = 0 0 + x = -70.710678119 + -150 x = -70.710678119 + -150 Combine like terms: -70.710678119 + -150 = -220.710678119 x = -220.710678119 Simplifying x = -220.710678119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-79.289321881, -220.710678119}
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