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Simplifying h2 + 28h + -3 = 0 Reorder the terms: -3 + 28h + h2 = 0 Solving -3 + 28h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 28h + 3 + h2 = 0 + 3 Reorder the terms: -3 + 3 + 28h + h2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 28h + h2 = 0 + 3 28h + h2 = 0 + 3 Combine like terms: 0 + 3 = 3 28h + h2 = 3 The h term is 28h. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28h + 196 + h2 = 3 + 196 Reorder the terms: 196 + 28h + h2 = 3 + 196 Combine like terms: 3 + 196 = 199 196 + 28h + h2 = 199 Factor a perfect square on the left side: (h + 14)(h + 14) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (h + 14) equal to 14.10673598 and -14.10673598.Subproblem 1
h + 14 = 14.10673598 Simplifying h + 14 = 14.10673598 Reorder the terms: 14 + h = 14.10673598 Solving 14 + h = 14.10673598 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = 14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + h = 14.10673598 + -14 h = 14.10673598 + -14 Combine like terms: 14.10673598 + -14 = 0.10673598 h = 0.10673598 Simplifying h = 0.10673598Subproblem 2
h + 14 = -14.10673598 Simplifying h + 14 = -14.10673598 Reorder the terms: 14 + h = -14.10673598 Solving 14 + h = -14.10673598 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = -14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + h = -14.10673598 + -14 h = -14.10673598 + -14 Combine like terms: -14.10673598 + -14 = -28.10673598 h = -28.10673598 Simplifying h = -28.10673598Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.10673598, -28.10673598}
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