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Simplifying h2 + -28h + -47 = 0 Reorder the terms: -47 + -28h + h2 = 0 Solving -47 + -28h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -28h + 47 + h2 = 0 + 47 Reorder the terms: -47 + 47 + -28h + h2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -28h + h2 = 0 + 47 -28h + h2 = 0 + 47 Combine like terms: 0 + 47 = 47 -28h + h2 = 47 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 = 47 + 196 Reorder the terms: 196 + -28h + h2 = 47 + 196 Combine like terms: 47 + 196 = 243 196 + -28h + h2 = 243 Factor a perfect square on the left side: (h + -14)(h + -14) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (h + -14) equal to 15.588457268 and -15.588457268.Subproblem 1
h + -14 = 15.588457268 Simplifying h + -14 = 15.588457268 Reorder the terms: -14 + h = 15.588457268 Solving -14 + h = 15.588457268 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 = 15.588457268 + 14 Combine like terms: -14 + 14 = 0 0 + h = 15.588457268 + 14 h = 15.588457268 + 14 Combine like terms: 15.588457268 + 14 = 29.588457268 h = 29.588457268 Simplifying h = 29.588457268Subproblem 2
h + -14 = -15.588457268 Simplifying h + -14 = -15.588457268 Reorder the terms: -14 + h = -15.588457268 Solving -14 + h = -15.588457268 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 = -15.588457268 + 14 Combine like terms: -14 + 14 = 0 0 + h = -15.588457268 + 14 h = -15.588457268 + 14 Combine like terms: -15.588457268 + 14 = -1.588457268 h = -1.588457268 Simplifying h = -1.588457268Solution
The solution to the problem is based on the solutions from the subproblems. h = {29.588457268, -1.588457268}
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