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Simplifying 500 = 50x + -8x2 Solving 500 = 50x + -8x2 Solving for variable 'x'. Reorder the terms: 500 + -50x + 8x2 = 50x + -50x + -8x2 + 8x2 Combine like terms: 50x + -50x = 0 500 + -50x + 8x2 = 0 + -8x2 + 8x2 500 + -50x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 500 + -50x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(250 + -25x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(250 + -25x + 4x2)' equal to zero and attempt to solve: Simplifying 250 + -25x + 4x2 = 0 Solving 250 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 62.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '-62.5' to each side of the equation. 62.5 + -6.25x + -62.5 + x2 = 0 + -62.5 Reorder the terms: 62.5 + -62.5 + -6.25x + x2 = 0 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + -6.25x + x2 = 0 + -62.5 -6.25x + x2 = 0 + -62.5 Combine like terms: 0 + -62.5 = -62.5 -6.25x + x2 = -62.5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -62.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -62.5 + 9.765625 Combine like terms: -62.5 + 9.765625 = -52.734375 9.765625 + -6.25x + x2 = -52.734375 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = -52.734375 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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