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Simplifying x2 + -150x + 300 = 0 Reorder the terms: 300 + -150x + x2 = 0 Solving 300 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -150x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -150x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -150x + x2 = 0 + -300 -150x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -150x + x2 = -300 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 = -300 + 5625 Reorder the terms: 5625 + -150x + x2 = -300 + 5625 Combine like terms: -300 + 5625 = 5325 5625 + -150x + x2 = 5325 Factor a perfect square on the left side: (x + -75)(x + -75) = 5325 Calculate the square root of the right side: 72.972597597 Break this problem into two subproblems by setting (x + -75) equal to 72.972597597 and -72.972597597.Subproblem 1
x + -75 = 72.972597597 Simplifying x + -75 = 72.972597597 Reorder the terms: -75 + x = 72.972597597 Solving -75 + x = 72.972597597 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 = 72.972597597 + 75 Combine like terms: -75 + 75 = 0 0 + x = 72.972597597 + 75 x = 72.972597597 + 75 Combine like terms: 72.972597597 + 75 = 147.972597597 x = 147.972597597 Simplifying x = 147.972597597Subproblem 2
x + -75 = -72.972597597 Simplifying x + -75 = -72.972597597 Reorder the terms: -75 + x = -72.972597597 Solving -75 + x = -72.972597597 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 = -72.972597597 + 75 Combine like terms: -75 + 75 = 0 0 + x = -72.972597597 + 75 x = -72.972597597 + 75 Combine like terms: -72.972597597 + 75 = 2.027402403 x = 2.027402403 Simplifying x = 2.027402403Solution
The solution to the problem is based on the solutions from the subproblems. x = {147.972597597, 2.027402403}
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