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Simplifying h2 + -19h + 52 = 0 Reorder the terms: 52 + -19h + h2 = 0 Solving 52 + -19h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -19h + -52 + h2 = 0 + -52 Reorder the terms: 52 + -52 + -19h + h2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -19h + h2 = 0 + -52 -19h + h2 = 0 + -52 Combine like terms: 0 + -52 = -52 -19h + h2 = -52 The h term is -19h. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19h + 90.25 + h2 = -52 + 90.25 Reorder the terms: 90.25 + -19h + h2 = -52 + 90.25 Combine like terms: -52 + 90.25 = 38.25 90.25 + -19h + h2 = 38.25 Factor a perfect square on the left side: (h + -9.5)(h + -9.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (h + -9.5) equal to 6.184658438 and -6.184658438.Subproblem 1
h + -9.5 = 6.184658438 Simplifying h + -9.5 = 6.184658438 Reorder the terms: -9.5 + h = 6.184658438 Solving -9.5 + h = 6.184658438 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + h = 6.184658438 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + h = 6.184658438 + 9.5 h = 6.184658438 + 9.5 Combine like terms: 6.184658438 + 9.5 = 15.684658438 h = 15.684658438 Simplifying h = 15.684658438Subproblem 2
h + -9.5 = -6.184658438 Simplifying h + -9.5 = -6.184658438 Reorder the terms: -9.5 + h = -6.184658438 Solving -9.5 + h = -6.184658438 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + h = -6.184658438 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + h = -6.184658438 + 9.5 h = -6.184658438 + 9.5 Combine like terms: -6.184658438 + 9.5 = 3.315341562 h = 3.315341562 Simplifying h = 3.315341562Solution
The solution to the problem is based on the solutions from the subproblems. h = {15.684658438, 3.315341562}
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