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Simplifying h2 + 22.4h = 1837 Reorder the terms: 22.4h + h2 = 1837 Solving 22.4h + h2 = 1837 Solving for variable 'h'. Reorder the terms: -1837 + 22.4h + h2 = 1837 + -1837 Combine like terms: 1837 + -1837 = 0 -1837 + 22.4h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '1837' to each side of the equation. -1837 + 22.4h + 1837 + h2 = 0 + 1837 Reorder the terms: -1837 + 1837 + 22.4h + h2 = 0 + 1837 Combine like terms: -1837 + 1837 = 0 0 + 22.4h + h2 = 0 + 1837 22.4h + h2 = 0 + 1837 Combine like terms: 0 + 1837 = 1837 22.4h + h2 = 1837 The h term is 22.4h. Take half its coefficient (11.2). Square it (125.44) and add it to both sides. Add '125.44' to each side of the equation. 22.4h + 125.44 + h2 = 1837 + 125.44 Reorder the terms: 125.44 + 22.4h + h2 = 1837 + 125.44 Combine like terms: 1837 + 125.44 = 1962.44 125.44 + 22.4h + h2 = 1962.44 Factor a perfect square on the left side: (h + 11.2)(h + 11.2) = 1962.44 Calculate the square root of the right side: 44.299435662 Break this problem into two subproblems by setting (h + 11.2) equal to 44.299435662 and -44.299435662.Subproblem 1
h + 11.2 = 44.299435662 Simplifying h + 11.2 = 44.299435662 Reorder the terms: 11.2 + h = 44.299435662 Solving 11.2 + h = 44.299435662 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11.2' to each side of the equation. 11.2 + -11.2 + h = 44.299435662 + -11.2 Combine like terms: 11.2 + -11.2 = 0.0 0.0 + h = 44.299435662 + -11.2 h = 44.299435662 + -11.2 Combine like terms: 44.299435662 + -11.2 = 33.099435662 h = 33.099435662 Simplifying h = 33.099435662Subproblem 2
h + 11.2 = -44.299435662 Simplifying h + 11.2 = -44.299435662 Reorder the terms: 11.2 + h = -44.299435662 Solving 11.2 + h = -44.299435662 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11.2' to each side of the equation. 11.2 + -11.2 + h = -44.299435662 + -11.2 Combine like terms: 11.2 + -11.2 = 0.0 0.0 + h = -44.299435662 + -11.2 h = -44.299435662 + -11.2 Combine like terms: -44.299435662 + -11.2 = -55.499435662 h = -55.499435662 Simplifying h = -55.499435662Solution
The solution to the problem is based on the solutions from the subproblems. h = {33.099435662, -55.499435662}
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