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Simplifying h2 + 2h + 4 = 170 Reorder the terms: 4 + 2h + h2 = 170 Solving 4 + 2h + h2 = 170 Solving for variable 'h'. Reorder the terms: 4 + -170 + 2h + h2 = 170 + -170 Combine like terms: 4 + -170 = -166 -166 + 2h + h2 = 170 + -170 Combine like terms: 170 + -170 = 0 -166 + 2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 2h + 166 + h2 = 0 + 166 Reorder the terms: -166 + 166 + 2h + h2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 2h + h2 = 0 + 166 2h + h2 = 0 + 166 Combine like terms: 0 + 166 = 166 2h + h2 = 166 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 = 166 + 1 Reorder the terms: 1 + 2h + h2 = 166 + 1 Combine like terms: 166 + 1 = 167 1 + 2h + h2 = 167 Factor a perfect square on the left side: (h + 1)(h + 1) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (h + 1) equal to 12.922847983 and -12.922847983.Subproblem 1
h + 1 = 12.922847983 Simplifying h + 1 = 12.922847983 Reorder the terms: 1 + h = 12.922847983 Solving 1 + h = 12.922847983 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 = 12.922847983 + -1 Combine like terms: 1 + -1 = 0 0 + h = 12.922847983 + -1 h = 12.922847983 + -1 Combine like terms: 12.922847983 + -1 = 11.922847983 h = 11.922847983 Simplifying h = 11.922847983Subproblem 2
h + 1 = -12.922847983 Simplifying h + 1 = -12.922847983 Reorder the terms: 1 + h = -12.922847983 Solving 1 + h = -12.922847983 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 = -12.922847983 + -1 Combine like terms: 1 + -1 = 0 0 + h = -12.922847983 + -1 h = -12.922847983 + -1 Combine like terms: -12.922847983 + -1 = -13.922847983 h = -13.922847983 Simplifying h = -13.922847983Solution
The solution to the problem is based on the solutions from the subproblems. h = {11.922847983, -13.922847983}
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