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Simplifying h2 + 6h + -21 = 0 Reorder the terms: -21 + 6h + h2 = 0 Solving -21 + 6h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 6h + 21 + h2 = 0 + 21 Reorder the terms: -21 + 21 + 6h + h2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 6h + h2 = 0 + 21 6h + h2 = 0 + 21 Combine like terms: 0 + 21 = 21 6h + h2 = 21 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 = 21 + 9 Reorder the terms: 9 + 6h + h2 = 21 + 9 Combine like terms: 21 + 9 = 30 9 + 6h + h2 = 30 Factor a perfect square on the left side: (h + 3)(h + 3) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (h + 3) equal to 5.477225575 and -5.477225575.Subproblem 1
h + 3 = 5.477225575 Simplifying h + 3 = 5.477225575 Reorder the terms: 3 + h = 5.477225575 Solving 3 + h = 5.477225575 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 = 5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + h = 5.477225575 + -3 h = 5.477225575 + -3 Combine like terms: 5.477225575 + -3 = 2.477225575 h = 2.477225575 Simplifying h = 2.477225575Subproblem 2
h + 3 = -5.477225575 Simplifying h + 3 = -5.477225575 Reorder the terms: 3 + h = -5.477225575 Solving 3 + h = -5.477225575 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 = -5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + h = -5.477225575 + -3 h = -5.477225575 + -3 Combine like terms: -5.477225575 + -3 = -8.477225575 h = -8.477225575 Simplifying h = -8.477225575Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.477225575, -8.477225575}
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