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Simplifying 1 = 2x2 + 16x + 310 Reorder the terms: 1 = 310 + 16x + 2x2 Solving 1 = 310 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 1 + -310 = -309 -309 + -16x + -2x2 = 310 + 16x + 2x2 + -310 + -16x + -2x2 Reorder the terms: -309 + -16x + -2x2 = 310 + -310 + 16x + -16x + 2x2 + -2x2 Combine like terms: 310 + -310 = 0 -309 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 -309 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 -309 + -16x + -2x2 = 0 + 2x2 + -2x2 -309 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -309 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(309 + 16x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(309 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying 309 + 16x + 2x2 = 0 Solving 309 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 154.5 + 8x + x2 = 0 Move the constant term to the right: Add '-154.5' to each side of the equation. 154.5 + 8x + -154.5 + x2 = 0 + -154.5 Reorder the terms: 154.5 + -154.5 + 8x + x2 = 0 + -154.5 Combine like terms: 154.5 + -154.5 = 0.0 0.0 + 8x + x2 = 0 + -154.5 8x + x2 = 0 + -154.5 Combine like terms: 0 + -154.5 = -154.5 8x + x2 = -154.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -154.5 + 16 Reorder the terms: 16 + 8x + x2 = -154.5 + 16 Combine like terms: -154.5 + 16 = -138.5 16 + 8x + x2 = -138.5 Factor a perfect square on the left side: (x + 4)(x + 4) = -138.5 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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