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Simplifying h2 + 2h = 45 Reorder the terms: 2h + h2 = 45 Solving 2h + h2 = 45 Solving for variable 'h'. Reorder the terms: -45 + 2h + h2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 2h + 45 + h2 = 0 + 45 Reorder the terms: -45 + 45 + 2h + h2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2h + h2 = 0 + 45 2h + h2 = 0 + 45 Combine like terms: 0 + 45 = 45 2h + h2 = 45 The h term is 2h. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2h + 1 + h2 = 45 + 1 Reorder the terms: 1 + 2h + h2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + 2h + h2 = 46 Factor a perfect square on the left side: (h + 1)(h + 1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (h + 1) equal to 6.782329983 and -6.782329983.Subproblem 1
h + 1 = 6.782329983 Simplifying h + 1 = 6.782329983 Reorder the terms: 1 + h = 6.782329983 Solving 1 + h = 6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + h = 6.782329983 + -1 h = 6.782329983 + -1 Combine like terms: 6.782329983 + -1 = 5.782329983 h = 5.782329983 Simplifying h = 5.782329983Subproblem 2
h + 1 = -6.782329983 Simplifying h + 1 = -6.782329983 Reorder the terms: 1 + h = -6.782329983 Solving 1 + h = -6.782329983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = -6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + h = -6.782329983 + -1 h = -6.782329983 + -1 Combine like terms: -6.782329983 + -1 = -7.782329983 h = -7.782329983 Simplifying h = -7.782329983Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.782329983, -7.782329983}
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