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Simplifying 11h2 + 7h + -12 = 0 Reorder the terms: -12 + 7h + 11h2 = 0 Solving -12 + 7h + 11h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.090909091 + 0.6363636364h + h2 = 0 Move the constant term to the right: Add '1.090909091' to each side of the equation. -1.090909091 + 0.6363636364h + 1.090909091 + h2 = 0 + 1.090909091 Reorder the terms: -1.090909091 + 1.090909091 + 0.6363636364h + h2 = 0 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + 0.6363636364h + h2 = 0 + 1.090909091 0.6363636364h + h2 = 0 + 1.090909091 Combine like terms: 0 + 1.090909091 = 1.090909091 0.6363636364h + h2 = 1.090909091 The h term is 0.6363636364h. Take half its coefficient (0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. 0.6363636364h + 0.1012396694 + h2 = 1.090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364h + h2 = 1.090909091 + 0.1012396694 Combine like terms: 1.090909091 + 0.1012396694 = 1.1921487604 0.1012396694 + 0.6363636364h + h2 = 1.1921487604 Factor a perfect square on the left side: (h + 0.3181818182)(h + 0.3181818182) = 1.1921487604 Calculate the square root of the right side: 1.09185565 Break this problem into two subproblems by setting (h + 0.3181818182) equal to 1.09185565 and -1.09185565.Subproblem 1
h + 0.3181818182 = 1.09185565 Simplifying h + 0.3181818182 = 1.09185565 Reorder the terms: 0.3181818182 + h = 1.09185565 Solving 0.3181818182 + h = 1.09185565 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + h = 1.09185565 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + h = 1.09185565 + -0.3181818182 h = 1.09185565 + -0.3181818182 Combine like terms: 1.09185565 + -0.3181818182 = 0.7736738318 h = 0.7736738318 Simplifying h = 0.7736738318Subproblem 2
h + 0.3181818182 = -1.09185565 Simplifying h + 0.3181818182 = -1.09185565 Reorder the terms: 0.3181818182 + h = -1.09185565 Solving 0.3181818182 + h = -1.09185565 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + h = -1.09185565 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + h = -1.09185565 + -0.3181818182 h = -1.09185565 + -0.3181818182 Combine like terms: -1.09185565 + -0.3181818182 = -1.4100374682 h = -1.4100374682 Simplifying h = -1.4100374682Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.7736738318, -1.4100374682}
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