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Simplifying x2 + -49x + 500 = 0 Reorder the terms: 500 + -49x + x2 = 0 Solving 500 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -49x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -49x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -49x + x2 = 0 + -500 -49x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -49x + x2 = -500 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = -500 + 600.25 Reorder the terms: 600.25 + -49x + x2 = -500 + 600.25 Combine like terms: -500 + 600.25 = 100.25 600.25 + -49x + x2 = 100.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -24.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -24.5 = 10.012492197 Simplifying x + -24.5 = 10.012492197 Reorder the terms: -24.5 + x = 10.012492197 Solving -24.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 10.012492197 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 10.012492197 + 24.5 x = 10.012492197 + 24.5 Combine like terms: 10.012492197 + 24.5 = 34.512492197 x = 34.512492197 Simplifying x = 34.512492197Subproblem 2
x + -24.5 = -10.012492197 Simplifying x + -24.5 = -10.012492197 Reorder the terms: -24.5 + x = -10.012492197 Solving -24.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -10.012492197 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -10.012492197 + 24.5 x = -10.012492197 + 24.5 Combine like terms: -10.012492197 + 24.5 = 14.487507803 x = 14.487507803 Simplifying x = 14.487507803Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.512492197, 14.487507803}
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