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Simplifying x2 + -150x + 540 = 0 Reorder the terms: 540 + -150x + x2 = 0 Solving 540 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-540' to each side of the equation. 540 + -150x + -540 + x2 = 0 + -540 Reorder the terms: 540 + -540 + -150x + x2 = 0 + -540 Combine like terms: 540 + -540 = 0 0 + -150x + x2 = 0 + -540 -150x + x2 = 0 + -540 Combine like terms: 0 + -540 = -540 -150x + x2 = -540 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 = -540 + 5625 Reorder the terms: 5625 + -150x + x2 = -540 + 5625 Combine like terms: -540 + 5625 = 5085 5625 + -150x + x2 = 5085 Factor a perfect square on the left side: (x + -75)(x + -75) = 5085 Calculate the square root of the right side: 71.309185944 Break this problem into two subproblems by setting (x + -75) equal to 71.309185944 and -71.309185944.Subproblem 1
x + -75 = 71.309185944 Simplifying x + -75 = 71.309185944 Reorder the terms: -75 + x = 71.309185944 Solving -75 + x = 71.309185944 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 = 71.309185944 + 75 Combine like terms: -75 + 75 = 0 0 + x = 71.309185944 + 75 x = 71.309185944 + 75 Combine like terms: 71.309185944 + 75 = 146.309185944 x = 146.309185944 Simplifying x = 146.309185944Subproblem 2
x + -75 = -71.309185944 Simplifying x + -75 = -71.309185944 Reorder the terms: -75 + x = -71.309185944 Solving -75 + x = -71.309185944 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 = -71.309185944 + 75 Combine like terms: -75 + 75 = 0 0 + x = -71.309185944 + 75 x = -71.309185944 + 75 Combine like terms: -71.309185944 + 75 = 3.690814056 x = 3.690814056 Simplifying x = 3.690814056Solution
The solution to the problem is based on the solutions from the subproblems. x = {146.309185944, 3.690814056}
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