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Simplifying 0 = 6x2 + x + 40000 Reorder the terms: 0 = 40000 + x + 6x2 Solving 0 = 40000 + x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -40000 = -40000 -40000 + -1x + -6x2 = 40000 + x + 6x2 + -40000 + -1x + -6x2 Reorder the terms: -40000 + -1x + -6x2 = 40000 + -40000 + x + -1x + 6x2 + -6x2 Combine like terms: 40000 + -40000 = 0 -40000 + -1x + -6x2 = 0 + x + -1x + 6x2 + -6x2 -40000 + -1x + -6x2 = x + -1x + 6x2 + -6x2 Combine like terms: x + -1x = 0 -40000 + -1x + -6x2 = 0 + 6x2 + -6x2 -40000 + -1x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -40000 + -1x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40000 + x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40000 + x + 6x2)' equal to zero and attempt to solve: Simplifying 40000 + x + 6x2 = 0 Solving 40000 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 6666.666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + 0.1666666667x + -6666.666667 + x2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + 0.1666666667x + x2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + 0.1666666667x + x2 = 0 + -6666.666667 0.1666666667x + x2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 0.1666666667x + x2 = -6666.666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = -6666.666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = -6666.666667 + 0.25 Combine like terms: -6666.666667 + 0.25 = -6666.416667 0.25 + 0.1666666667x + x2 = -6666.416667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -6666.416667 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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