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Simplifying 0 = 16X2 + 90X + 12000 Reorder the terms: 0 = 12000 + 90X + 16X2 Solving 0 = 12000 + 90X + 16X2 Solving for variable 'X'. Combine like terms: 0 + -12000 = -12000 -12000 + -90X + -16X2 = 12000 + 90X + 16X2 + -12000 + -90X + -16X2 Reorder the terms: -12000 + -90X + -16X2 = 12000 + -12000 + 90X + -90X + 16X2 + -16X2 Combine like terms: 12000 + -12000 = 0 -12000 + -90X + -16X2 = 0 + 90X + -90X + 16X2 + -16X2 -12000 + -90X + -16X2 = 90X + -90X + 16X2 + -16X2 Combine like terms: 90X + -90X = 0 -12000 + -90X + -16X2 = 0 + 16X2 + -16X2 -12000 + -90X + -16X2 = 16X2 + -16X2 Combine like terms: 16X2 + -16X2 = 0 -12000 + -90X + -16X2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(6000 + 45X + 8X2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6000 + 45X + 8X2)' equal to zero and attempt to solve: Simplifying 6000 + 45X + 8X2 = 0 Solving 6000 + 45X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 750 + 5.625X + X2 = 0 Move the constant term to the right: Add '-750' to each side of the equation. 750 + 5.625X + -750 + X2 = 0 + -750 Reorder the terms: 750 + -750 + 5.625X + X2 = 0 + -750 Combine like terms: 750 + -750 = 0 0 + 5.625X + X2 = 0 + -750 5.625X + X2 = 0 + -750 Combine like terms: 0 + -750 = -750 5.625X + X2 = -750 The X term is 5.625X. Take half its coefficient (2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. 5.625X + 7.91015625 + X2 = -750 + 7.91015625 Reorder the terms: 7.91015625 + 5.625X + X2 = -750 + 7.91015625 Combine like terms: -750 + 7.91015625 = -742.08984375 7.91015625 + 5.625X + X2 = -742.08984375 Factor a perfect square on the left side: (X + 2.8125)(X + 2.8125) = -742.08984375 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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