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Simplifying h2 + 24h + -9 = 0 Reorder the terms: -9 + 24h + h2 = 0 Solving -9 + 24h + 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 + 24h + 9 + h2 = 0 + 9 Reorder the terms: -9 + 9 + 24h + h2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 24h + h2 = 0 + 9 24h + h2 = 0 + 9 Combine like terms: 0 + 9 = 9 24h + h2 = 9 The h term is 24h. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24h + 144 + h2 = 9 + 144 Reorder the terms: 144 + 24h + h2 = 9 + 144 Combine like terms: 9 + 144 = 153 144 + 24h + h2 = 153 Factor a perfect square on the left side: (h + 12)(h + 12) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (h + 12) equal to 12.369316877 and -12.369316877.Subproblem 1
h + 12 = 12.369316877 Simplifying h + 12 = 12.369316877 Reorder the terms: 12 + h = 12.369316877 Solving 12 + h = 12.369316877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + h = 12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + h = 12.369316877 + -12 h = 12.369316877 + -12 Combine like terms: 12.369316877 + -12 = 0.369316877 h = 0.369316877 Simplifying h = 0.369316877Subproblem 2
h + 12 = -12.369316877 Simplifying h + 12 = -12.369316877 Reorder the terms: 12 + h = -12.369316877 Solving 12 + h = -12.369316877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + h = -12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + h = -12.369316877 + -12 h = -12.369316877 + -12 Combine like terms: -12.369316877 + -12 = -24.369316877 h = -24.369316877 Simplifying h = -24.369316877Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.369316877, -24.369316877}
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