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Simplifying h2 + 22h = 1837 Reorder the terms: 22h + h2 = 1837 Solving 22h + h2 = 1837 Solving for variable 'h'. Reorder the terms: -1837 + 22h + h2 = 1837 + -1837 Combine like terms: 1837 + -1837 = 0 -1837 + 22h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '1837' to each side of the equation. -1837 + 22h + 1837 + h2 = 0 + 1837 Reorder the terms: -1837 + 1837 + 22h + h2 = 0 + 1837 Combine like terms: -1837 + 1837 = 0 0 + 22h + h2 = 0 + 1837 22h + h2 = 0 + 1837 Combine like terms: 0 + 1837 = 1837 22h + h2 = 1837 The h term is 22h. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22h + 121 + h2 = 1837 + 121 Reorder the terms: 121 + 22h + h2 = 1837 + 121 Combine like terms: 1837 + 121 = 1958 121 + 22h + h2 = 1958 Factor a perfect square on the left side: (h + 11)(h + 11) = 1958 Calculate the square root of the right side: 44.24929378 Break this problem into two subproblems by setting (h + 11) equal to 44.24929378 and -44.24929378.Subproblem 1
h + 11 = 44.24929378 Simplifying h + 11 = 44.24929378 Reorder the terms: 11 + h = 44.24929378 Solving 11 + h = 44.24929378 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + h = 44.24929378 + -11 Combine like terms: 11 + -11 = 0 0 + h = 44.24929378 + -11 h = 44.24929378 + -11 Combine like terms: 44.24929378 + -11 = 33.24929378 h = 33.24929378 Simplifying h = 33.24929378Subproblem 2
h + 11 = -44.24929378 Simplifying h + 11 = -44.24929378 Reorder the terms: 11 + h = -44.24929378 Solving 11 + h = -44.24929378 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + h = -44.24929378 + -11 Combine like terms: 11 + -11 = 0 0 + h = -44.24929378 + -11 h = -44.24929378 + -11 Combine like terms: -44.24929378 + -11 = -55.24929378 h = -55.24929378 Simplifying h = -55.24929378Solution
The solution to the problem is based on the solutions from the subproblems. h = {33.24929378, -55.24929378}
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