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Simplifying -4h(5h + 7) + 16h = 40 Reorder the terms: -4h(7 + 5h) + 16h = 40 (7 * -4h + 5h * -4h) + 16h = 40 (-28h + -20h2) + 16h = 40 Reorder the terms: -28h + 16h + -20h2 = 40 Combine like terms: -28h + 16h = -12h -12h + -20h2 = 40 Solving -12h + -20h2 = 40 Solving for variable 'h'. Reorder the terms: -40 + -12h + -20h2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -12h + -20h2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(10 + 3h + 5h2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(10 + 3h + 5h2)' equal to zero and attempt to solve: Simplifying 10 + 3h + 5h2 = 0 Solving 10 + 3h + 5h2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 0.6h + h2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.6h + -2 + h2 = 0 + -2 Reorder the terms: 2 + -2 + 0.6h + h2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.6h + h2 = 0 + -2 0.6h + h2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.6h + h2 = -2 The h term is 0.6h. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6h + 0.09 + h2 = -2 + 0.09 Reorder the terms: 0.09 + 0.6h + h2 = -2 + 0.09 Combine like terms: -2 + 0.09 = -1.91 0.09 + 0.6h + h2 = -1.91 Factor a perfect square on the left side: (h + 0.3)(h + 0.3) = -1.91 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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