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Simplifying h2 + -8h + -49 = 0 Reorder the terms: -49 + -8h + h2 = 0 Solving -49 + -8h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -8h + 49 + h2 = 0 + 49 Reorder the terms: -49 + 49 + -8h + h2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -8h + h2 = 0 + 49 -8h + h2 = 0 + 49 Combine like terms: 0 + 49 = 49 -8h + h2 = 49 The h term is -8h. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8h + 16 + h2 = 49 + 16 Reorder the terms: 16 + -8h + h2 = 49 + 16 Combine like terms: 49 + 16 = 65 16 + -8h + h2 = 65 Factor a perfect square on the left side: (h + -4)(h + -4) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (h + -4) equal to 8.062257748 and -8.062257748.Subproblem 1
h + -4 = 8.062257748 Simplifying h + -4 = 8.062257748 Reorder the terms: -4 + h = 8.062257748 Solving -4 + h = 8.062257748 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = 8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + h = 8.062257748 + 4 h = 8.062257748 + 4 Combine like terms: 8.062257748 + 4 = 12.062257748 h = 12.062257748 Simplifying h = 12.062257748Subproblem 2
h + -4 = -8.062257748 Simplifying h + -4 = -8.062257748 Reorder the terms: -4 + h = -8.062257748 Solving -4 + h = -8.062257748 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = -8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + h = -8.062257748 + 4 h = -8.062257748 + 4 Combine like terms: -8.062257748 + 4 = -4.062257748 h = -4.062257748 Simplifying h = -4.062257748Solution
The solution to the problem is based on the solutions from the subproblems. h = {12.062257748, -4.062257748}
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