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Simplifying 50x + -2x2 = 50 Solving 50x + -2x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 50x + -2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 50x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 25x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 25x + -1x2)' equal to zero and attempt to solve: Simplifying -25 + 25x + -1x2 = 0 Solving -25 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -25x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -25x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -25x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -25x + x2 = 0 + -25 -25x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -25x + x2 = -25 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -25 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -25 + 156.25 Combine like terms: -25 + 156.25 = 131.25 156.25 + -25x + x2 = 131.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + -12.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + -12.5 = 11.456439237 Simplifying x + -12.5 = 11.456439237 Reorder the terms: -12.5 + x = 11.456439237 Solving -12.5 + x = 11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 11.456439237 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.456439237 + 12.5 x = 11.456439237 + 12.5 Combine like terms: 11.456439237 + 12.5 = 23.956439237 x = 23.956439237 Simplifying x = 23.956439237Subproblem 2
x + -12.5 = -11.456439237 Simplifying x + -12.5 = -11.456439237 Reorder the terms: -12.5 + x = -11.456439237 Solving -12.5 + x = -11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -11.456439237 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.456439237 + 12.5 x = -11.456439237 + 12.5 Combine like terms: -11.456439237 + 12.5 = 1.043560763 x = 1.043560763 Simplifying x = 1.043560763Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.956439237, 1.043560763}Solution
x = {23.956439237, 1.043560763}
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