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Simplifying h2 + 7h + -21 = 0 Reorder the terms: -21 + 7h + h2 = 0 Solving -21 + 7h + 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 + 7h + 21 + h2 = 0 + 21 Reorder the terms: -21 + 21 + 7h + h2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 7h + h2 = 0 + 21 7h + h2 = 0 + 21 Combine like terms: 0 + 21 = 21 7h + h2 = 21 The h term is 7h. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7h + 12.25 + h2 = 21 + 12.25 Reorder the terms: 12.25 + 7h + h2 = 21 + 12.25 Combine like terms: 21 + 12.25 = 33.25 12.25 + 7h + h2 = 33.25 Factor a perfect square on the left side: (h + 3.5)(h + 3.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (h + 3.5) equal to 5.766281297 and -5.766281297.Subproblem 1
h + 3.5 = 5.766281297 Simplifying h + 3.5 = 5.766281297 Reorder the terms: 3.5 + h = 5.766281297 Solving 3.5 + h = 5.766281297 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = 5.766281297 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 5.766281297 + -3.5 h = 5.766281297 + -3.5 Combine like terms: 5.766281297 + -3.5 = 2.266281297 h = 2.266281297 Simplifying h = 2.266281297Subproblem 2
h + 3.5 = -5.766281297 Simplifying h + 3.5 = -5.766281297 Reorder the terms: 3.5 + h = -5.766281297 Solving 3.5 + h = -5.766281297 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = -5.766281297 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -5.766281297 + -3.5 h = -5.766281297 + -3.5 Combine like terms: -5.766281297 + -3.5 = -9.266281297 h = -9.266281297 Simplifying h = -9.266281297Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.266281297, -9.266281297}
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