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Simplifying 0 = 2x2 + -25x + -250 Reorder the terms: 0 = -250 + -25x + 2x2 Solving 0 = -250 + -25x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 250 = 250 250 + 25x + -2x2 = -250 + -25x + 2x2 + 250 + 25x + -2x2 Reorder the terms: 250 + 25x + -2x2 = -250 + 250 + -25x + 25x + 2x2 + -2x2 Combine like terms: -250 + 250 = 0 250 + 25x + -2x2 = 0 + -25x + 25x + 2x2 + -2x2 250 + 25x + -2x2 = -25x + 25x + 2x2 + -2x2 Combine like terms: -25x + 25x = 0 250 + 25x + -2x2 = 0 + 2x2 + -2x2 250 + 25x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 250 + 25x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -125 + -12.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -12.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -12.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -12.5x + x2 = 0 + 125 -12.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -12.5x + x2 = 125 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 125 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 125 + 39.0625 Combine like terms: 125 + 39.0625 = 164.0625 39.0625 + -12.5x + x2 = 164.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 164.0625 Calculate the square root of the right side: 12.808688457 Break this problem into two subproblems by setting (x + -6.25) equal to 12.808688457 and -12.808688457.Subproblem 1
x + -6.25 = 12.808688457 Simplifying x + -6.25 = 12.808688457 Reorder the terms: -6.25 + x = 12.808688457 Solving -6.25 + x = 12.808688457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 12.808688457 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 12.808688457 + 6.25 x = 12.808688457 + 6.25 Combine like terms: 12.808688457 + 6.25 = 19.058688457 x = 19.058688457 Simplifying x = 19.058688457Subproblem 2
x + -6.25 = -12.808688457 Simplifying x + -6.25 = -12.808688457 Reorder the terms: -6.25 + x = -12.808688457 Solving -6.25 + x = -12.808688457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -12.808688457 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -12.808688457 + 6.25 x = -12.808688457 + 6.25 Combine like terms: -12.808688457 + 6.25 = -6.558688457 x = -6.558688457 Simplifying x = -6.558688457Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.058688457, -6.558688457}
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