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Simplifying x2 + 150x + 500 = 0 Reorder the terms: 500 + 150x + x2 = 0 Solving 500 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 150x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 150x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 150x + x2 = 0 + -500 150x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 150x + x2 = -500 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 = -500 + 5625 Reorder the terms: 5625 + 150x + x2 = -500 + 5625 Combine like terms: -500 + 5625 = 5125 5625 + 150x + x2 = 5125 Factor a perfect square on the left side: (x + 75)(x + 75) = 5125 Calculate the square root of the right side: 71.589105316 Break this problem into two subproblems by setting (x + 75) equal to 71.589105316 and -71.589105316.Subproblem 1
x + 75 = 71.589105316 Simplifying x + 75 = 71.589105316 Reorder the terms: 75 + x = 71.589105316 Solving 75 + x = 71.589105316 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 = 71.589105316 + -75 Combine like terms: 75 + -75 = 0 0 + x = 71.589105316 + -75 x = 71.589105316 + -75 Combine like terms: 71.589105316 + -75 = -3.410894684 x = -3.410894684 Simplifying x = -3.410894684Subproblem 2
x + 75 = -71.589105316 Simplifying x + 75 = -71.589105316 Reorder the terms: 75 + x = -71.589105316 Solving 75 + x = -71.589105316 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 = -71.589105316 + -75 Combine like terms: 75 + -75 = 0 0 + x = -71.589105316 + -75 x = -71.589105316 + -75 Combine like terms: -71.589105316 + -75 = -146.589105316 x = -146.589105316 Simplifying x = -146.589105316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.410894684, -146.589105316}
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