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Simplifying 0 = 2x2 + 25x + 5000 Reorder the terms: 0 = 5000 + 25x + 2x2 Solving 0 = 5000 + 25x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -5000 = -5000 -5000 + -25x + -2x2 = 5000 + 25x + 2x2 + -5000 + -25x + -2x2 Reorder the terms: -5000 + -25x + -2x2 = 5000 + -5000 + 25x + -25x + 2x2 + -2x2 Combine like terms: 5000 + -5000 = 0 -5000 + -25x + -2x2 = 0 + 25x + -25x + 2x2 + -2x2 -5000 + -25x + -2x2 = 25x + -25x + 2x2 + -2x2 Combine like terms: 25x + -25x = 0 -5000 + -25x + -2x2 = 0 + 2x2 + -2x2 -5000 + -25x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5000 + -25x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5000 + 25x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5000 + 25x + 2x2)' equal to zero and attempt to solve: Simplifying 5000 + 25x + 2x2 = 0 Solving 5000 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2500 + 12.5x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + 12.5x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + 12.5x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + 12.5x + x2 = 0 + -2500 12.5x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 12.5x + x2 = -2500 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 = -2500 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -2500 + 39.0625 Combine like terms: -2500 + 39.0625 = -2460.9375 39.0625 + 12.5x + x2 = -2460.9375 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = -2460.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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