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Simplifying 50x + -25 = 2x2 + -2x Reorder the terms: -25 + 50x = 2x2 + -2x Reorder the terms: -25 + 50x = -2x + 2x2 Solving -25 + 50x = -2x + 2x2 Solving for variable 'x'. Combine like terms: 50x + 2x = 52x -25 + 52x + -2x2 = -2x + 2x2 + 2x + -2x2 Reorder the terms: -25 + 52x + -2x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -25 + 52x + -2x2 = 0 + 2x2 + -2x2 -25 + 52x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -25 + 52x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 12.5 + -26x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -26x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -26x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -26x + x2 = 0 + -12.5 -26x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -26x + x2 = -12.5 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -12.5 + 169 Reorder the terms: 169 + -26x + x2 = -12.5 + 169 Combine like terms: -12.5 + 169 = 156.5 169 + -26x + x2 = 156.5 Factor a perfect square on the left side: (x + -13)(x + -13) = 156.5 Calculate the square root of the right side: 12.509996003 Break this problem into two subproblems by setting (x + -13) equal to 12.509996003 and -12.509996003.Subproblem 1
x + -13 = 12.509996003 Simplifying x + -13 = 12.509996003 Reorder the terms: -13 + x = 12.509996003 Solving -13 + x = 12.509996003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.509996003 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.509996003 + 13 x = 12.509996003 + 13 Combine like terms: 12.509996003 + 13 = 25.509996003 x = 25.509996003 Simplifying x = 25.509996003Subproblem 2
x + -13 = -12.509996003 Simplifying x + -13 = -12.509996003 Reorder the terms: -13 + x = -12.509996003 Solving -13 + x = -12.509996003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.509996003 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.509996003 + 13 x = -12.509996003 + 13 Combine like terms: -12.509996003 + 13 = 0.490003997 x = 0.490003997 Simplifying x = 0.490003997Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.509996003, 0.490003997}
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