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Simplifying -16x2 + 112x + 2 = 338 Reorder the terms: 2 + 112x + -16x2 = 338 Solving 2 + 112x + -16x2 = 338 Solving for variable 'x'. Reorder the terms: 2 + -338 + 112x + -16x2 = 338 + -338 Combine like terms: 2 + -338 = -336 -336 + 112x + -16x2 = 338 + -338 Combine like terms: 338 + -338 = 0 -336 + 112x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-21 + 7x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-21 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -21 + 7x + -1x2 = 0 Solving -21 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + -7x + x2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -7x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -7x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -7x + x2 = 0 + -21 -7x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -7x + x2 = -21 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -21 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -21 + 12.25 Combine like terms: -21 + 12.25 = -8.75 12.25 + -7x + x2 = -8.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -8.75 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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