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Simplifying h2 + 28h + -14 = 0 Reorder the terms: -14 + 28h + h2 = 0 Solving -14 + 28h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 28h + 14 + h2 = 0 + 14 Reorder the terms: -14 + 14 + 28h + h2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 28h + h2 = 0 + 14 28h + h2 = 0 + 14 Combine like terms: 0 + 14 = 14 28h + h2 = 14 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 = 14 + 196 Reorder the terms: 196 + 28h + h2 = 14 + 196 Combine like terms: 14 + 196 = 210 196 + 28h + h2 = 210 Factor a perfect square on the left side: (h + 14)(h + 14) = 210 Calculate the square root of the right side: 14.491376746 Break this problem into two subproblems by setting (h + 14) equal to 14.491376746 and -14.491376746.Subproblem 1
h + 14 = 14.491376746 Simplifying h + 14 = 14.491376746 Reorder the terms: 14 + h = 14.491376746 Solving 14 + h = 14.491376746 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 = 14.491376746 + -14 Combine like terms: 14 + -14 = 0 0 + h = 14.491376746 + -14 h = 14.491376746 + -14 Combine like terms: 14.491376746 + -14 = 0.491376746 h = 0.491376746 Simplifying h = 0.491376746Subproblem 2
h + 14 = -14.491376746 Simplifying h + 14 = -14.491376746 Reorder the terms: 14 + h = -14.491376746 Solving 14 + h = -14.491376746 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 = -14.491376746 + -14 Combine like terms: 14 + -14 = 0 0 + h = -14.491376746 + -14 h = -14.491376746 + -14 Combine like terms: -14.491376746 + -14 = -28.491376746 h = -28.491376746 Simplifying h = -28.491376746Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.491376746, -28.491376746}
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