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Simplifying 68 = 441 + 2x + 2x2 Solving 68 = 441 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 68 + -441 = -373 -373 + -2x + -2x2 = 441 + 2x + 2x2 + -441 + -2x + -2x2 Reorder the terms: -373 + -2x + -2x2 = 441 + -441 + 2x + -2x + 2x2 + -2x2 Combine like terms: 441 + -441 = 0 -373 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 -373 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 -373 + -2x + -2x2 = 0 + 2x2 + -2x2 -373 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -373 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(373 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(373 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 373 + 2x + 2x2 = 0 Solving 373 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 186.5 + x + x2 = 0 Move the constant term to the right: Add '-186.5' to each side of the equation. 186.5 + x + -186.5 + x2 = 0 + -186.5 Reorder the terms: 186.5 + -186.5 + x + x2 = 0 + -186.5 Combine like terms: 186.5 + -186.5 = 0.0 0.0 + x + x2 = 0 + -186.5 x + x2 = 0 + -186.5 Combine like terms: 0 + -186.5 = -186.5 x + x2 = -186.5 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. + 0.25 + x2 = -186.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -186.5 + 0.25 Combine like terms: -186.5 + 0.25 = -186.25 1.25 + x2 = -186.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -186.25 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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