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Simplifying h2 + 20h = 49 Reorder the terms: 20h + h2 = 49 Solving 20h + h2 = 49 Solving for variable 'h'. Reorder the terms: -49 + 20h + h2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 20h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 20h + 49 + h2 = 0 + 49 Reorder the terms: -49 + 49 + 20h + h2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 20h + h2 = 0 + 49 20h + h2 = 0 + 49 Combine like terms: 0 + 49 = 49 20h + h2 = 49 The h term is 20h. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20h + 100 + h2 = 49 + 100 Reorder the terms: 100 + 20h + h2 = 49 + 100 Combine like terms: 49 + 100 = 149 100 + 20h + h2 = 149 Factor a perfect square on the left side: (h + 10)(h + 10) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (h + 10) equal to 12.206555616 and -12.206555616.Subproblem 1
h + 10 = 12.206555616 Simplifying h + 10 = 12.206555616 Reorder the terms: 10 + h = 12.206555616 Solving 10 + h = 12.206555616 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = 12.206555616 + -10 Combine like terms: 10 + -10 = 0 0 + h = 12.206555616 + -10 h = 12.206555616 + -10 Combine like terms: 12.206555616 + -10 = 2.206555616 h = 2.206555616 Simplifying h = 2.206555616Subproblem 2
h + 10 = -12.206555616 Simplifying h + 10 = -12.206555616 Reorder the terms: 10 + h = -12.206555616 Solving 10 + h = -12.206555616 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = -12.206555616 + -10 Combine like terms: 10 + -10 = 0 0 + h = -12.206555616 + -10 h = -12.206555616 + -10 Combine like terms: -12.206555616 + -10 = -22.206555616 h = -22.206555616 Simplifying h = -22.206555616Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.206555616, -22.206555616}
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