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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 = 6250 5625 + -150x + x2 = 6250 Factor a perfect square on the left side: (x + -75)(x + -75) = 6250 Calculate the square root of the right side: 79.056941504 Break this problem into two subproblems by setting (x + -75) equal to 79.056941504 and -79.056941504.Subproblem 1
x + -75 = 79.056941504 Simplifying x + -75 = 79.056941504 Reorder the terms: -75 + x = 79.056941504 Solving -75 + x = 79.056941504 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 = 79.056941504 + 75 Combine like terms: -75 + 75 = 0 0 + x = 79.056941504 + 75 x = 79.056941504 + 75 Combine like terms: 79.056941504 + 75 = 154.056941504 x = 154.056941504 Simplifying x = 154.056941504Subproblem 2
x + -75 = -79.056941504 Simplifying x + -75 = -79.056941504 Reorder the terms: -75 + x = -79.056941504 Solving -75 + x = -79.056941504 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 = -79.056941504 + 75 Combine like terms: -75 + 75 = 0 0 + x = -79.056941504 + 75 x = -79.056941504 + 75 Combine like terms: -79.056941504 + 75 = -4.056941504 x = -4.056941504 Simplifying x = -4.056941504Solution
The solution to the problem is based on the solutions from the subproblems. x = {154.056941504, -4.056941504}
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