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Simplifying h2 + 24h = 7 Reorder the terms: 24h + h2 = 7 Solving 24h + h2 = 7 Solving for variable 'h'. Reorder the terms: -7 + 24h + h2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 24h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 24h + 7 + h2 = 0 + 7 Reorder the terms: -7 + 7 + 24h + h2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 24h + h2 = 0 + 7 24h + h2 = 0 + 7 Combine like terms: 0 + 7 = 7 24h + h2 = 7 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 = 7 + 144 Reorder the terms: 144 + 24h + h2 = 7 + 144 Combine like terms: 7 + 144 = 151 144 + 24h + h2 = 151 Factor a perfect square on the left side: (h + 12)(h + 12) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (h + 12) equal to 12.288205727 and -12.288205727.Subproblem 1
h + 12 = 12.288205727 Simplifying h + 12 = 12.288205727 Reorder the terms: 12 + h = 12.288205727 Solving 12 + h = 12.288205727 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 = 12.288205727 + -12 Combine like terms: 12 + -12 = 0 0 + h = 12.288205727 + -12 h = 12.288205727 + -12 Combine like terms: 12.288205727 + -12 = 0.288205727 h = 0.288205727 Simplifying h = 0.288205727Subproblem 2
h + 12 = -12.288205727 Simplifying h + 12 = -12.288205727 Reorder the terms: 12 + h = -12.288205727 Solving 12 + h = -12.288205727 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 = -12.288205727 + -12 Combine like terms: 12 + -12 = 0 0 + h = -12.288205727 + -12 h = -12.288205727 + -12 Combine like terms: -12.288205727 + -12 = -24.288205727 h = -24.288205727 Simplifying h = -24.288205727Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.288205727, -24.288205727}
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