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Simplifying 16x + -2x2 = 82 Solving 16x + -2x2 = 82 Solving for variable 'x'. Reorder the terms: -82 + 16x + -2x2 = 82 + -82 Combine like terms: 82 + -82 = 0 -82 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -41 + 8x + -1x2 = 0 Solving -41 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 41 + -8x + x2 = 0 Move the constant term to the right: Add '-41' to each side of the equation. 41 + -8x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -8x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -8x + x2 = 0 + -41 -8x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -8x + x2 = -41 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 = -41 + 16 Reorder the terms: 16 + -8x + x2 = -41 + 16 Combine like terms: -41 + 16 = -25 16 + -8x + x2 = -25 Factor a perfect square on the left side: (x + -4)(x + -4) = -25 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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