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Simplifying x2 + 50x + -672 = 0 Reorder the terms: -672 + 50x + x2 = 0 Solving -672 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '672' to each side of the equation. -672 + 50x + 672 + x2 = 0 + 672 Reorder the terms: -672 + 672 + 50x + x2 = 0 + 672 Combine like terms: -672 + 672 = 0 0 + 50x + x2 = 0 + 672 50x + x2 = 0 + 672 Combine like terms: 0 + 672 = 672 50x + x2 = 672 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 = 672 + 625 Reorder the terms: 625 + 50x + x2 = 672 + 625 Combine like terms: 672 + 625 = 1297 625 + 50x + x2 = 1297 Factor a perfect square on the left side: (x + 25)(x + 25) = 1297 Calculate the square root of the right side: 36.013886211 Break this problem into two subproblems by setting (x + 25) equal to 36.013886211 and -36.013886211.Subproblem 1
x + 25 = 36.013886211 Simplifying x + 25 = 36.013886211 Reorder the terms: 25 + x = 36.013886211 Solving 25 + x = 36.013886211 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 = 36.013886211 + -25 Combine like terms: 25 + -25 = 0 0 + x = 36.013886211 + -25 x = 36.013886211 + -25 Combine like terms: 36.013886211 + -25 = 11.013886211 x = 11.013886211 Simplifying x = 11.013886211Subproblem 2
x + 25 = -36.013886211 Simplifying x + 25 = -36.013886211 Reorder the terms: 25 + x = -36.013886211 Solving 25 + x = -36.013886211 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 = -36.013886211 + -25 Combine like terms: 25 + -25 = 0 0 + x = -36.013886211 + -25 x = -36.013886211 + -25 Combine like terms: -36.013886211 + -25 = -61.013886211 x = -61.013886211 Simplifying x = -61.013886211Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.013886211, -61.013886211}
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