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Simplifying h2 + 2h = 27 Reorder the terms: 2h + h2 = 27 Solving 2h + h2 = 27 Solving for variable 'h'. Reorder the terms: -27 + 2h + h2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 2h + 27 + h2 = 0 + 27 Reorder the terms: -27 + 27 + 2h + h2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 2h + h2 = 0 + 27 2h + h2 = 0 + 27 Combine like terms: 0 + 27 = 27 2h + h2 = 27 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 = 27 + 1 Reorder the terms: 1 + 2h + h2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + 2h + h2 = 28 Factor a perfect square on the left side: (h + 1)(h + 1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (h + 1) equal to 5.291502622 and -5.291502622.Subproblem 1
h + 1 = 5.291502622 Simplifying h + 1 = 5.291502622 Reorder the terms: 1 + h = 5.291502622 Solving 1 + h = 5.291502622 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 = 5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + h = 5.291502622 + -1 h = 5.291502622 + -1 Combine like terms: 5.291502622 + -1 = 4.291502622 h = 4.291502622 Simplifying h = 4.291502622Subproblem 2
h + 1 = -5.291502622 Simplifying h + 1 = -5.291502622 Reorder the terms: 1 + h = -5.291502622 Solving 1 + h = -5.291502622 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 = -5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + h = -5.291502622 + -1 h = -5.291502622 + -1 Combine like terms: -5.291502622 + -1 = -6.291502622 h = -6.291502622 Simplifying h = -6.291502622Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.291502622, -6.291502622}
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