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Simplifying h2 + 9h + 1 = 8 Reorder the terms: 1 + 9h + h2 = 8 Solving 1 + 9h + h2 = 8 Solving for variable 'h'. Reorder the terms: 1 + -8 + 9h + h2 = 8 + -8 Combine like terms: 1 + -8 = -7 -7 + 9h + h2 = 8 + -8 Combine like terms: 8 + -8 = 0 -7 + 9h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 9h + 7 + h2 = 0 + 7 Reorder the terms: -7 + 7 + 9h + h2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9h + h2 = 0 + 7 9h + h2 = 0 + 7 Combine like terms: 0 + 7 = 7 9h + h2 = 7 The h term is 9h. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9h + 20.25 + h2 = 7 + 20.25 Reorder the terms: 20.25 + 9h + h2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + 9h + h2 = 27.25 Factor a perfect square on the left side: (h + 4.5)(h + 4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (h + 4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
h + 4.5 = 5.220153254 Simplifying h + 4.5 = 5.220153254 Reorder the terms: 4.5 + h = 5.220153254 Solving 4.5 + h = 5.220153254 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + h = 5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + h = 5.220153254 + -4.5 h = 5.220153254 + -4.5 Combine like terms: 5.220153254 + -4.5 = 0.720153254 h = 0.720153254 Simplifying h = 0.720153254Subproblem 2
h + 4.5 = -5.220153254 Simplifying h + 4.5 = -5.220153254 Reorder the terms: 4.5 + h = -5.220153254 Solving 4.5 + h = -5.220153254 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + h = -5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + h = -5.220153254 + -4.5 h = -5.220153254 + -4.5 Combine like terms: -5.220153254 + -4.5 = -9.720153254 h = -9.720153254 Simplifying h = -9.720153254Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.720153254, -9.720153254}
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