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Simplifying h2 + 49 = 16h Reorder the terms: 49 + h2 = 16h Solving 49 + h2 = 16h Solving for variable 'h'. Reorder the terms: 49 + -16h + h2 = 16h + -16h Combine like terms: 16h + -16h = 0 49 + -16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -16h + -49 + h2 = 0 + -49 Reorder the terms: 49 + -49 + -16h + h2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -16h + h2 = 0 + -49 -16h + h2 = 0 + -49 Combine like terms: 0 + -49 = -49 -16h + h2 = -49 The h term is -16h. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16h + 64 + h2 = -49 + 64 Reorder the terms: 64 + -16h + h2 = -49 + 64 Combine like terms: -49 + 64 = 15 64 + -16h + h2 = 15 Factor a perfect square on the left side: (h + -8)(h + -8) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (h + -8) equal to 3.872983346 and -3.872983346.Subproblem 1
h + -8 = 3.872983346 Simplifying h + -8 = 3.872983346 Reorder the terms: -8 + h = 3.872983346 Solving -8 + h = 3.872983346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = 3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + h = 3.872983346 + 8 h = 3.872983346 + 8 Combine like terms: 3.872983346 + 8 = 11.872983346 h = 11.872983346 Simplifying h = 11.872983346Subproblem 2
h + -8 = -3.872983346 Simplifying h + -8 = -3.872983346 Reorder the terms: -8 + h = -3.872983346 Solving -8 + h = -3.872983346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = -3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + h = -3.872983346 + 8 h = -3.872983346 + 8 Combine like terms: -3.872983346 + 8 = 4.127016654 h = 4.127016654 Simplifying h = 4.127016654Solution
The solution to the problem is based on the solutions from the subproblems. h = {11.872983346, 4.127016654}
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