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Simplifying h2 + 6h + -51 = 0 Reorder the terms: -51 + 6h + h2 = 0 Solving -51 + 6h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 6h + 51 + h2 = 0 + 51 Reorder the terms: -51 + 51 + 6h + h2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 6h + h2 = 0 + 51 6h + h2 = 0 + 51 Combine like terms: 0 + 51 = 51 6h + h2 = 51 The h term is 6h. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6h + 9 + h2 = 51 + 9 Reorder the terms: 9 + 6h + h2 = 51 + 9 Combine like terms: 51 + 9 = 60 9 + 6h + h2 = 60 Factor a perfect square on the left side: (h + 3)(h + 3) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (h + 3) equal to 7.745966692 and -7.745966692.Subproblem 1
h + 3 = 7.745966692 Simplifying h + 3 = 7.745966692 Reorder the terms: 3 + h = 7.745966692 Solving 3 + h = 7.745966692 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = 7.745966692 + -3 Combine like terms: 3 + -3 = 0 0 + h = 7.745966692 + -3 h = 7.745966692 + -3 Combine like terms: 7.745966692 + -3 = 4.745966692 h = 4.745966692 Simplifying h = 4.745966692Subproblem 2
h + 3 = -7.745966692 Simplifying h + 3 = -7.745966692 Reorder the terms: 3 + h = -7.745966692 Solving 3 + h = -7.745966692 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = -7.745966692 + -3 Combine like terms: 3 + -3 = 0 0 + h = -7.745966692 + -3 h = -7.745966692 + -3 Combine like terms: -7.745966692 + -3 = -10.745966692 h = -10.745966692 Simplifying h = -10.745966692Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.745966692, -10.745966692}
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