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Simplifying 50x + -1x2 = 25 Solving 50x + -1x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 50x + -1x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -50x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -50x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -50x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -50x + x2 = 0 + -25 -50x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -50x + x2 = -25 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 = -25 + 625 Reorder the terms: 625 + -50x + x2 = -25 + 625 Combine like terms: -25 + 625 = 600 625 + -50x + x2 = 600 Factor a perfect square on the left side: (x + -25)(x + -25) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + -25) equal to 24.494897428 and -24.494897428.Subproblem 1
x + -25 = 24.494897428 Simplifying x + -25 = 24.494897428 Reorder the terms: -25 + x = 24.494897428 Solving -25 + x = 24.494897428 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 = 24.494897428 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.494897428 + 25 x = 24.494897428 + 25 Combine like terms: 24.494897428 + 25 = 49.494897428 x = 49.494897428 Simplifying x = 49.494897428Subproblem 2
x + -25 = -24.494897428 Simplifying x + -25 = -24.494897428 Reorder the terms: -25 + x = -24.494897428 Solving -25 + x = -24.494897428 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 = -24.494897428 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.494897428 + 25 x = -24.494897428 + 25 Combine like terms: -24.494897428 + 25 = 0.505102572 x = 0.505102572 Simplifying x = 0.505102572Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.494897428, 0.505102572}
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