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Simplifying 0 = 16x2 + 62x + 199 Reorder the terms: 0 = 199 + 62x + 16x2 Solving 0 = 199 + 62x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -199 = -199 -199 + -62x + -16x2 = 199 + 62x + 16x2 + -199 + -62x + -16x2 Reorder the terms: -199 + -62x + -16x2 = 199 + -199 + 62x + -62x + 16x2 + -16x2 Combine like terms: 199 + -199 = 0 -199 + -62x + -16x2 = 0 + 62x + -62x + 16x2 + -16x2 -199 + -62x + -16x2 = 62x + -62x + 16x2 + -16x2 Combine like terms: 62x + -62x = 0 -199 + -62x + -16x2 = 0 + 16x2 + -16x2 -199 + -62x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -199 + -62x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(199 + 62x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(199 + 62x + 16x2)' equal to zero and attempt to solve: Simplifying 199 + 62x + 16x2 = 0 Solving 199 + 62x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 12.4375 + 3.875x + x2 = 0 Move the constant term to the right: Add '-12.4375' to each side of the equation. 12.4375 + 3.875x + -12.4375 + x2 = 0 + -12.4375 Reorder the terms: 12.4375 + -12.4375 + 3.875x + x2 = 0 + -12.4375 Combine like terms: 12.4375 + -12.4375 = 0.0000 0.0000 + 3.875x + x2 = 0 + -12.4375 3.875x + x2 = 0 + -12.4375 Combine like terms: 0 + -12.4375 = -12.4375 3.875x + x2 = -12.4375 The x term is 3.875x. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875x + 3.75390625 + x2 = -12.4375 + 3.75390625 Reorder the terms: 3.75390625 + 3.875x + x2 = -12.4375 + 3.75390625 Combine like terms: -12.4375 + 3.75390625 = -8.68359375 3.75390625 + 3.875x + x2 = -8.68359375 Factor a perfect square on the left side: (x + 1.9375)(x + 1.9375) = -8.68359375 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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