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Simplifying 7(8 + -6h) * h = 5 Reorder the terms for easier multiplication: 7h(8 + -6h) = 5 (8 * 7h + -6h * 7h) = 5 (56h + -42h2) = 5 Solving 56h + -42h2 = 5 Solving for variable 'h'. Reorder the terms: -5 + 56h + -42h2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 56h + -42h2 = 0 Begin completing the square. Divide all terms by -42 the coefficient of the squared term: Divide each side by '-42'. 0.119047619 + -1.333333333h + h2 = 0 Move the constant term to the right: Add '-0.119047619' to each side of the equation. 0.119047619 + -1.333333333h + -0.119047619 + h2 = 0 + -0.119047619 Reorder the terms: 0.119047619 + -0.119047619 + -1.333333333h + h2 = 0 + -0.119047619 Combine like terms: 0.119047619 + -0.119047619 = 0.000000000 0.000000000 + -1.333333333h + h2 = 0 + -0.119047619 -1.333333333h + h2 = 0 + -0.119047619 Combine like terms: 0 + -0.119047619 = -0.119047619 -1.333333333h + h2 = -0.119047619 The h term is -1.333333333h. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333h + 0.4444444442 + h2 = -0.119047619 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333h + h2 = -0.119047619 + 0.4444444442 Combine like terms: -0.119047619 + 0.4444444442 = 0.3253968252 0.4444444442 + -1.333333333h + h2 = 0.3253968252 Factor a perfect square on the left side: (h + -0.6666666665)(h + -0.6666666665) = 0.3253968252 Calculate the square root of the right side: 0.570435645 Break this problem into two subproblems by setting (h + -0.6666666665) equal to 0.570435645 and -0.570435645.Subproblem 1
h + -0.6666666665 = 0.570435645 Simplifying h + -0.6666666665 = 0.570435645 Reorder the terms: -0.6666666665 + h = 0.570435645 Solving -0.6666666665 + h = 0.570435645 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + h = 0.570435645 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + h = 0.570435645 + 0.6666666665 h = 0.570435645 + 0.6666666665 Combine like terms: 0.570435645 + 0.6666666665 = 1.2371023115 h = 1.2371023115 Simplifying h = 1.2371023115Subproblem 2
h + -0.6666666665 = -0.570435645 Simplifying h + -0.6666666665 = -0.570435645 Reorder the terms: -0.6666666665 + h = -0.570435645 Solving -0.6666666665 + h = -0.570435645 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + h = -0.570435645 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + h = -0.570435645 + 0.6666666665 h = -0.570435645 + 0.6666666665 Combine like terms: -0.570435645 + 0.6666666665 = 0.0962310215 h = 0.0962310215 Simplifying h = 0.0962310215Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.2371023115, 0.0962310215}
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