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Simplifying h2 + -24h + 1 = 0 Reorder the terms: 1 + -24h + h2 = 0 Solving 1 + -24h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -24h + -1 + h2 = 0 + -1 Reorder the terms: 1 + -1 + -24h + h2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -24h + h2 = 0 + -1 -24h + h2 = 0 + -1 Combine like terms: 0 + -1 = -1 -24h + h2 = -1 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 = -1 + 144 Reorder the terms: 144 + -24h + h2 = -1 + 144 Combine like terms: -1 + 144 = 143 144 + -24h + h2 = 143 Factor a perfect square on the left side: (h + -12)(h + -12) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (h + -12) equal to 11.958260743 and -11.958260743.Subproblem 1
h + -12 = 11.958260743 Simplifying h + -12 = 11.958260743 Reorder the terms: -12 + h = 11.958260743 Solving -12 + h = 11.958260743 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 = 11.958260743 + 12 Combine like terms: -12 + 12 = 0 0 + h = 11.958260743 + 12 h = 11.958260743 + 12 Combine like terms: 11.958260743 + 12 = 23.958260743 h = 23.958260743 Simplifying h = 23.958260743Subproblem 2
h + -12 = -11.958260743 Simplifying h + -12 = -11.958260743 Reorder the terms: -12 + h = -11.958260743 Solving -12 + h = -11.958260743 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 = -11.958260743 + 12 Combine like terms: -12 + 12 = 0 0 + h = -11.958260743 + 12 h = -11.958260743 + 12 Combine like terms: -11.958260743 + 12 = 0.041739257 h = 0.041739257 Simplifying h = 0.041739257Solution
The solution to the problem is based on the solutions from the subproblems. h = {23.958260743, 0.041739257}
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