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Simplifying h2 + 5h = 225 Reorder the terms: 5h + h2 = 225 Solving 5h + h2 = 225 Solving for variable 'h'. Reorder the terms: -225 + 5h + h2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 5h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 5h + 225 + h2 = 0 + 225 Reorder the terms: -225 + 225 + 5h + h2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 5h + h2 = 0 + 225 5h + h2 = 0 + 225 Combine like terms: 0 + 225 = 225 5h + h2 = 225 The h term is 5h. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5h + 6.25 + h2 = 225 + 6.25 Reorder the terms: 6.25 + 5h + h2 = 225 + 6.25 Combine like terms: 225 + 6.25 = 231.25 6.25 + 5h + h2 = 231.25 Factor a perfect square on the left side: (h + 2.5)(h + 2.5) = 231.25 Calculate the square root of the right side: 15.206906326 Break this problem into two subproblems by setting (h + 2.5) equal to 15.206906326 and -15.206906326.Subproblem 1
h + 2.5 = 15.206906326 Simplifying h + 2.5 = 15.206906326 Reorder the terms: 2.5 + h = 15.206906326 Solving 2.5 + h = 15.206906326 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = 15.206906326 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 15.206906326 + -2.5 h = 15.206906326 + -2.5 Combine like terms: 15.206906326 + -2.5 = 12.706906326 h = 12.706906326 Simplifying h = 12.706906326Subproblem 2
h + 2.5 = -15.206906326 Simplifying h + 2.5 = -15.206906326 Reorder the terms: 2.5 + h = -15.206906326 Solving 2.5 + h = -15.206906326 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = -15.206906326 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -15.206906326 + -2.5 h = -15.206906326 + -2.5 Combine like terms: -15.206906326 + -2.5 = -17.706906326 h = -17.706906326 Simplifying h = -17.706906326Solution
The solution to the problem is based on the solutions from the subproblems. h = {12.706906326, -17.706906326}
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