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Simplifying h2 + 17h + -9 = 0 Reorder the terms: -9 + 17h + h2 = 0 Solving -9 + 17h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 17h + 9 + h2 = 0 + 9 Reorder the terms: -9 + 9 + 17h + h2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 17h + h2 = 0 + 9 17h + h2 = 0 + 9 Combine like terms: 0 + 9 = 9 17h + h2 = 9 The h term is 17h. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17h + 72.25 + h2 = 9 + 72.25 Reorder the terms: 72.25 + 17h + h2 = 9 + 72.25 Combine like terms: 9 + 72.25 = 81.25 72.25 + 17h + h2 = 81.25 Factor a perfect square on the left side: (h + 8.5)(h + 8.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (h + 8.5) equal to 9.013878189 and -9.013878189.Subproblem 1
h + 8.5 = 9.013878189 Simplifying h + 8.5 = 9.013878189 Reorder the terms: 8.5 + h = 9.013878189 Solving 8.5 + h = 9.013878189 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + h = 9.013878189 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + h = 9.013878189 + -8.5 h = 9.013878189 + -8.5 Combine like terms: 9.013878189 + -8.5 = 0.513878189 h = 0.513878189 Simplifying h = 0.513878189Subproblem 2
h + 8.5 = -9.013878189 Simplifying h + 8.5 = -9.013878189 Reorder the terms: 8.5 + h = -9.013878189 Solving 8.5 + h = -9.013878189 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + h = -9.013878189 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + h = -9.013878189 + -8.5 h = -9.013878189 + -8.5 Combine like terms: -9.013878189 + -8.5 = -17.513878189 h = -17.513878189 Simplifying h = -17.513878189Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.513878189, -17.513878189}
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