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Simplifying -2x2 + 100x + -25 = 0 Reorder the terms: -25 + 100x + -2x2 = 0 Solving -25 + 100x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 12.5 + -50x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -50x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -50x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -50x + x2 = 0 + -12.5 -50x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -50x + x2 = -12.5 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 = -12.5 + 625 Reorder the terms: 625 + -50x + x2 = -12.5 + 625 Combine like terms: -12.5 + 625 = 612.5 625 + -50x + x2 = 612.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 612.5 Calculate the square root of the right side: 24.748737342 Break this problem into two subproblems by setting (x + -25) equal to 24.748737342 and -24.748737342.Subproblem 1
x + -25 = 24.748737342 Simplifying x + -25 = 24.748737342 Reorder the terms: -25 + x = 24.748737342 Solving -25 + x = 24.748737342 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 = 24.748737342 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.748737342 + 25 x = 24.748737342 + 25 Combine like terms: 24.748737342 + 25 = 49.748737342 x = 49.748737342 Simplifying x = 49.748737342Subproblem 2
x + -25 = -24.748737342 Simplifying x + -25 = -24.748737342 Reorder the terms: -25 + x = -24.748737342 Solving -25 + x = -24.748737342 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 = -24.748737342 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.748737342 + 25 x = -24.748737342 + 25 Combine like terms: -24.748737342 + 25 = 0.251262658 x = 0.251262658 Simplifying x = 0.251262658Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.748737342, 0.251262658}
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