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Simplifying -17 = 2h2 + 7h Reorder the terms: -17 = 7h + 2h2 Solving -17 = 7h + 2h2 Solving for variable 'h'. Reorder the terms: -17 + -7h + -2h2 = 7h + -7h + 2h2 + -2h2 Combine like terms: 7h + -7h = 0 -17 + -7h + -2h2 = 0 + 2h2 + -2h2 -17 + -7h + -2h2 = 2h2 + -2h2 Combine like terms: 2h2 + -2h2 = 0 -17 + -7h + -2h2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 7h + 2h2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 7h + 2h2)' equal to zero and attempt to solve: Simplifying 17 + 7h + 2h2 = 0 Solving 17 + 7h + 2h2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 3.5h + h2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 3.5h + -8.5 + h2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 3.5h + h2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 3.5h + h2 = 0 + -8.5 3.5h + h2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 3.5h + h2 = -8.5 The h term is 3.5h. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5h + 3.0625 + h2 = -8.5 + 3.0625 Reorder the terms: 3.0625 + 3.5h + h2 = -8.5 + 3.0625 Combine like terms: -8.5 + 3.0625 = -5.4375 3.0625 + 3.5h + h2 = -5.4375 Factor a perfect square on the left side: (h + 1.75)(h + 1.75) = -5.4375 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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