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Simplifying x2 + -150x + 625 = 0 Reorder the terms: 625 + -150x + x2 = 0 Solving 625 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-625' to each side of the equation. 625 + -150x + -625 + x2 = 0 + -625 Reorder the terms: 625 + -625 + -150x + x2 = 0 + -625 Combine like terms: 625 + -625 = 0 0 + -150x + x2 = 0 + -625 -150x + x2 = 0 + -625 Combine like terms: 0 + -625 = -625 -150x + x2 = -625 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 = -625 + 5625 Reorder the terms: 5625 + -150x + x2 = -625 + 5625 Combine like terms: -625 + 5625 = 5000 5625 + -150x + x2 = 5000 Factor a perfect square on the left side: (x + -75)(x + -75) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + -75) equal to 70.710678119 and -70.710678119.Subproblem 1
x + -75 = 70.710678119 Simplifying x + -75 = 70.710678119 Reorder the terms: -75 + x = 70.710678119 Solving -75 + x = 70.710678119 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 = 70.710678119 + 75 Combine like terms: -75 + 75 = 0 0 + x = 70.710678119 + 75 x = 70.710678119 + 75 Combine like terms: 70.710678119 + 75 = 145.710678119 x = 145.710678119 Simplifying x = 145.710678119Subproblem 2
x + -75 = -70.710678119 Simplifying x + -75 = -70.710678119 Reorder the terms: -75 + x = -70.710678119 Solving -75 + x = -70.710678119 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 = -70.710678119 + 75 Combine like terms: -75 + 75 = 0 0 + x = -70.710678119 + 75 x = -70.710678119 + 75 Combine like terms: -70.710678119 + 75 = 4.289321881 x = 4.289321881 Simplifying x = 4.289321881Solution
The solution to the problem is based on the solutions from the subproblems. x = {145.710678119, 4.289321881}
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