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Simplifying 2h2 = h2 + 2h + 17 Reorder the terms: 2h2 = 17 + 2h + h2 Solving 2h2 = 17 + 2h + h2 Solving for variable 'h'. Reorder the terms: -17 + -2h + 2h2 + -1h2 = 17 + 2h + h2 + -17 + -2h + -1h2 Combine like terms: 2h2 + -1h2 = 1h2 -17 + -2h + 1h2 = 17 + 2h + h2 + -17 + -2h + -1h2 Reorder the terms: -17 + -2h + 1h2 = 17 + -17 + 2h + -2h + h2 + -1h2 Combine like terms: 17 + -17 = 0 -17 + -2h + 1h2 = 0 + 2h + -2h + h2 + -1h2 -17 + -2h + 1h2 = 2h + -2h + h2 + -1h2 Combine like terms: 2h + -2h = 0 -17 + -2h + 1h2 = 0 + h2 + -1h2 -17 + -2h + 1h2 = h2 + -1h2 Combine like terms: h2 + -1h2 = 0 -17 + -2h + 1h2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -2h + 17 + h2 = 0 + 17 Reorder the terms: -17 + 17 + -2h + h2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2h + h2 = 0 + 17 -2h + h2 = 0 + 17 Combine like terms: 0 + 17 = 17 -2h + h2 = 17 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 = 17 + 1 Reorder the terms: 1 + -2h + h2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + -2h + h2 = 18 Factor a perfect square on the left side: (h + -1)(h + -1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (h + -1) equal to 4.242640687 and -4.242640687.Subproblem 1
h + -1 = 4.242640687 Simplifying h + -1 = 4.242640687 Reorder the terms: -1 + h = 4.242640687 Solving -1 + h = 4.242640687 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 = 4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + h = 4.242640687 + 1 h = 4.242640687 + 1 Combine like terms: 4.242640687 + 1 = 5.242640687 h = 5.242640687 Simplifying h = 5.242640687Subproblem 2
h + -1 = -4.242640687 Simplifying h + -1 = -4.242640687 Reorder the terms: -1 + h = -4.242640687 Solving -1 + h = -4.242640687 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 = -4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + h = -4.242640687 + 1 h = -4.242640687 + 1 Combine like terms: -4.242640687 + 1 = -3.242640687 h = -3.242640687 Simplifying h = -3.242640687Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.242640687, -3.242640687}
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