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Simplifying 0 = 4x2 + 29x + 68 Reorder the terms: 0 = 68 + 29x + 4x2 Solving 0 = 68 + 29x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -68 = -68 -68 + -29x + -4x2 = 68 + 29x + 4x2 + -68 + -29x + -4x2 Reorder the terms: -68 + -29x + -4x2 = 68 + -68 + 29x + -29x + 4x2 + -4x2 Combine like terms: 68 + -68 = 0 -68 + -29x + -4x2 = 0 + 29x + -29x + 4x2 + -4x2 -68 + -29x + -4x2 = 29x + -29x + 4x2 + -4x2 Combine like terms: 29x + -29x = 0 -68 + -29x + -4x2 = 0 + 4x2 + -4x2 -68 + -29x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -68 + -29x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(68 + 29x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(68 + 29x + 4x2)' equal to zero and attempt to solve: Simplifying 68 + 29x + 4x2 = 0 Solving 68 + 29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 17 + 7.25x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + 7.25x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 7.25x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 7.25x + x2 = 0 + -17 7.25x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 7.25x + x2 = -17 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = -17 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = -17 + 13.140625 Combine like terms: -17 + 13.140625 = -3.859375 13.140625 + 7.25x + x2 = -3.859375 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = -3.859375 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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