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Simplifying 0 = 8x2 + -50x + 1000 Reorder the terms: 0 = 1000 + -50x + 8x2 Solving 0 = 1000 + -50x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + 50x + -8x2 = 1000 + -50x + 8x2 + -1000 + 50x + -8x2 Reorder the terms: -1000 + 50x + -8x2 = 1000 + -1000 + -50x + 50x + 8x2 + -8x2 Combine like terms: 1000 + -1000 = 0 -1000 + 50x + -8x2 = 0 + -50x + 50x + 8x2 + -8x2 -1000 + 50x + -8x2 = -50x + 50x + 8x2 + -8x2 Combine like terms: -50x + 50x = 0 -1000 + 50x + -8x2 = 0 + 8x2 + -8x2 -1000 + 50x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -1000 + 50x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 25x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 25x + -4x2)' equal to zero and attempt to solve: Simplifying -500 + 25x + -4x2 = 0 Solving -500 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 125 + -6.25x + x2 = 0 Move the constant term to the right: Add '-125' to each side of the equation. 125 + -6.25x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + -6.25x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -6.25x + x2 = 0 + -125 -6.25x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 -6.25x + x2 = -125 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 = -125 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -125 + 9.765625 Combine like terms: -125 + 9.765625 = -115.234375 9.765625 + -6.25x + x2 = -115.234375 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = -115.234375 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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