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Simplifying h * h + 10h = 21 Multiply h * h h2 + 10h = 21 Reorder the terms: 10h + h2 = 21 Solving 10h + h2 = 21 Solving for variable 'h'. Reorder the terms: -21 + 10h + h2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 10h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 10h + 21 + h2 = 0 + 21 Reorder the terms: -21 + 21 + 10h + h2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 10h + h2 = 0 + 21 10h + h2 = 0 + 21 Combine like terms: 0 + 21 = 21 10h + h2 = 21 The h term is 10h. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10h + 25 + h2 = 21 + 25 Reorder the terms: 25 + 10h + h2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + 10h + h2 = 46 Factor a perfect square on the left side: (h + 5)(h + 5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (h + 5) equal to 6.782329983 and -6.782329983.Subproblem 1
h + 5 = 6.782329983 Simplifying h + 5 = 6.782329983 Reorder the terms: 5 + h = 6.782329983 Solving 5 + h = 6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + h = 6.782329983 + -5 h = 6.782329983 + -5 Combine like terms: 6.782329983 + -5 = 1.782329983 h = 1.782329983 Simplifying h = 1.782329983Subproblem 2
h + 5 = -6.782329983 Simplifying h + 5 = -6.782329983 Reorder the terms: 5 + h = -6.782329983 Solving 5 + h = -6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + h = -6.782329983 + -5 h = -6.782329983 + -5 Combine like terms: -6.782329983 + -5 = -11.782329983 h = -11.782329983 Simplifying h = -11.782329983Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.782329983, -11.782329983}
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