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Simplifying 12x2 + -250x + 5000 = 0 Reorder the terms: 5000 + -250x + 12x2 = 0 Solving 5000 + -250x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2500 + -125x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2500 + -125x + 6x2)' equal to zero and attempt to solve: Simplifying 2500 + -125x + 6x2 = 0 Solving 2500 + -125x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 416.6666667 + -20.83333333x + x2 = 0 Move the constant term to the right: Add '-416.6666667' to each side of the equation. 416.6666667 + -20.83333333x + -416.6666667 + x2 = 0 + -416.6666667 Reorder the terms: 416.6666667 + -416.6666667 + -20.83333333x + x2 = 0 + -416.6666667 Combine like terms: 416.6666667 + -416.6666667 = 0.0000000 0.0000000 + -20.83333333x + x2 = 0 + -416.6666667 -20.83333333x + x2 = 0 + -416.6666667 Combine like terms: 0 + -416.6666667 = -416.6666667 -20.83333333x + x2 = -416.6666667 The x term is -20.83333333x. Take half its coefficient (-10.41666667). Square it (108.5069445) and add it to both sides. Add '108.5069445' to each side of the equation. -20.83333333x + 108.5069445 + x2 = -416.6666667 + 108.5069445 Reorder the terms: 108.5069445 + -20.83333333x + x2 = -416.6666667 + 108.5069445 Combine like terms: -416.6666667 + 108.5069445 = -308.1597222 108.5069445 + -20.83333333x + x2 = -308.1597222 Factor a perfect square on the left side: (x + -10.41666667)(x + -10.41666667) = -308.1597222 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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