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Simplifying h2 + 8h + -750 = 0 Reorder the terms: -750 + 8h + h2 = 0 Solving -750 + 8h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + 8h + 750 + h2 = 0 + 750 Reorder the terms: -750 + 750 + 8h + h2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + 8h + h2 = 0 + 750 8h + h2 = 0 + 750 Combine like terms: 0 + 750 = 750 8h + h2 = 750 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 = 750 + 16 Reorder the terms: 16 + 8h + h2 = 750 + 16 Combine like terms: 750 + 16 = 766 16 + 8h + h2 = 766 Factor a perfect square on the left side: (h + 4)(h + 4) = 766 Calculate the square root of the right side: 27.676705006 Break this problem into two subproblems by setting (h + 4) equal to 27.676705006 and -27.676705006.Subproblem 1
h + 4 = 27.676705006 Simplifying h + 4 = 27.676705006 Reorder the terms: 4 + h = 27.676705006 Solving 4 + h = 27.676705006 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 = 27.676705006 + -4 Combine like terms: 4 + -4 = 0 0 + h = 27.676705006 + -4 h = 27.676705006 + -4 Combine like terms: 27.676705006 + -4 = 23.676705006 h = 23.676705006 Simplifying h = 23.676705006Subproblem 2
h + 4 = -27.676705006 Simplifying h + 4 = -27.676705006 Reorder the terms: 4 + h = -27.676705006 Solving 4 + h = -27.676705006 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 = -27.676705006 + -4 Combine like terms: 4 + -4 = 0 0 + h = -27.676705006 + -4 h = -27.676705006 + -4 Combine like terms: -27.676705006 + -4 = -31.676705006 h = -31.676705006 Simplifying h = -31.676705006Solution
The solution to the problem is based on the solutions from the subproblems. h = {23.676705006, -31.676705006}
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