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Simplifying 2h2 + 12h + 9 = 0 Reorder the terms: 9 + 12h + 2h2 = 0 Solving 9 + 12h + 2h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 6h + h2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 6h + -4.5 + h2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 6h + h2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 6h + h2 = 0 + -4.5 6h + h2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 6h + h2 = -4.5 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 = -4.5 + 9 Reorder the terms: 9 + 6h + h2 = -4.5 + 9 Combine like terms: -4.5 + 9 = 4.5 9 + 6h + h2 = 4.5 Factor a perfect square on the left side: (h + 3)(h + 3) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (h + 3) equal to 2.121320344 and -2.121320344.Subproblem 1
h + 3 = 2.121320344 Simplifying h + 3 = 2.121320344 Reorder the terms: 3 + h = 2.121320344 Solving 3 + h = 2.121320344 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 = 2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + h = 2.121320344 + -3 h = 2.121320344 + -3 Combine like terms: 2.121320344 + -3 = -0.878679656 h = -0.878679656 Simplifying h = -0.878679656Subproblem 2
h + 3 = -2.121320344 Simplifying h + 3 = -2.121320344 Reorder the terms: 3 + h = -2.121320344 Solving 3 + h = -2.121320344 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 = -2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + h = -2.121320344 + -3 h = -2.121320344 + -3 Combine like terms: -2.121320344 + -3 = -5.121320344 h = -5.121320344 Simplifying h = -5.121320344Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.878679656, -5.121320344}
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