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Simplifying -5x + 3 = 16x2 + 56 + 49 Reorder the terms: 3 + -5x = 16x2 + 56 + 49 Reorder the terms: 3 + -5x = 56 + 49 + 16x2 Combine like terms: 56 + 49 = 105 3 + -5x = 105 + 16x2 Solving 3 + -5x = 105 + 16x2 Solving for variable 'x'. Reorder the terms: 3 + -105 + -5x + -16x2 = 105 + 16x2 + -105 + -16x2 Combine like terms: 3 + -105 = -102 -102 + -5x + -16x2 = 105 + 16x2 + -105 + -16x2 Reorder the terms: -102 + -5x + -16x2 = 105 + -105 + 16x2 + -16x2 Combine like terms: 105 + -105 = 0 -102 + -5x + -16x2 = 0 + 16x2 + -16x2 -102 + -5x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -102 + -5x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(102 + 5x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(102 + 5x + 16x2)' equal to zero and attempt to solve: Simplifying 102 + 5x + 16x2 = 0 Solving 102 + 5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 6.375 + 0.3125x + x2 = 0 Move the constant term to the right: Add '-6.375' to each side of the equation. 6.375 + 0.3125x + -6.375 + x2 = 0 + -6.375 Reorder the terms: 6.375 + -6.375 + 0.3125x + x2 = 0 + -6.375 Combine like terms: 6.375 + -6.375 = 0.000 0.000 + 0.3125x + x2 = 0 + -6.375 0.3125x + x2 = 0 + -6.375 Combine like terms: 0 + -6.375 = -6.375 0.3125x + x2 = -6.375 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = -6.375 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = -6.375 + 0.0244140625 Combine like terms: -6.375 + 0.0244140625 = -6.3505859375 0.0244140625 + 0.3125x + x2 = -6.3505859375 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = -6.3505859375 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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