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Simplifying x2 + 50x + -760 = 0 Reorder the terms: -760 + 50x + x2 = 0 Solving -760 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '760' to each side of the equation. -760 + 50x + 760 + x2 = 0 + 760 Reorder the terms: -760 + 760 + 50x + x2 = 0 + 760 Combine like terms: -760 + 760 = 0 0 + 50x + x2 = 0 + 760 50x + x2 = 0 + 760 Combine like terms: 0 + 760 = 760 50x + x2 = 760 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 760 + 625 Reorder the terms: 625 + 50x + x2 = 760 + 625 Combine like terms: 760 + 625 = 1385 625 + 50x + x2 = 1385 Factor a perfect square on the left side: (x + 25)(x + 25) = 1385 Calculate the square root of the right side: 37.215588132 Break this problem into two subproblems by setting (x + 25) equal to 37.215588132 and -37.215588132.Subproblem 1
x + 25 = 37.215588132 Simplifying x + 25 = 37.215588132 Reorder the terms: 25 + x = 37.215588132 Solving 25 + x = 37.215588132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 37.215588132 + -25 Combine like terms: 25 + -25 = 0 0 + x = 37.215588132 + -25 x = 37.215588132 + -25 Combine like terms: 37.215588132 + -25 = 12.215588132 x = 12.215588132 Simplifying x = 12.215588132Subproblem 2
x + 25 = -37.215588132 Simplifying x + 25 = -37.215588132 Reorder the terms: 25 + x = -37.215588132 Solving 25 + x = -37.215588132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -37.215588132 + -25 Combine like terms: 25 + -25 = 0 0 + x = -37.215588132 + -25 x = -37.215588132 + -25 Combine like terms: -37.215588132 + -25 = -62.215588132 x = -62.215588132 Simplifying x = -62.215588132Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.215588132, -62.215588132}
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