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Simplifying 0.5h2 + 3h + -77 = 0 Reorder the terms: -77 + 3h + 0.5h2 = 0 Solving -77 + 3h + 0.5h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -154 + 6h + h2 = 0 Move the constant term to the right: Add '154' to each side of the equation. -154 + 6h + 154 + h2 = 0 + 154 Reorder the terms: -154 + 154 + 6h + h2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 6h + h2 = 0 + 154 6h + h2 = 0 + 154 Combine like terms: 0 + 154 = 154 6h + h2 = 154 The h term is 6h. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6h + 9 + h2 = 154 + 9 Reorder the terms: 9 + 6h + h2 = 154 + 9 Combine like terms: 154 + 9 = 163 9 + 6h + h2 = 163 Factor a perfect square on the left side: (h + 3)(h + 3) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (h + 3) equal to 12.767145335 and -12.767145335.Subproblem 1
h + 3 = 12.767145335 Simplifying h + 3 = 12.767145335 Reorder the terms: 3 + h = 12.767145335 Solving 3 + h = 12.767145335 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = 12.767145335 + -3 Combine like terms: 3 + -3 = 0 0 + h = 12.767145335 + -3 h = 12.767145335 + -3 Combine like terms: 12.767145335 + -3 = 9.767145335 h = 9.767145335 Simplifying h = 9.767145335Subproblem 2
h + 3 = -12.767145335 Simplifying h + 3 = -12.767145335 Reorder the terms: 3 + h = -12.767145335 Solving 3 + h = -12.767145335 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = -12.767145335 + -3 Combine like terms: 3 + -3 = 0 0 + h = -12.767145335 + -3 h = -12.767145335 + -3 Combine like terms: -12.767145335 + -3 = -15.767145335 h = -15.767145335 Simplifying h = -15.767145335Solution
The solution to the problem is based on the solutions from the subproblems. h = {9.767145335, -15.767145335}
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