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Simplifying 2h2 + 7h + 3 = 20 Reorder the terms: 3 + 7h + 2h2 = 20 Solving 3 + 7h + 2h2 = 20 Solving for variable 'h'. Reorder the terms: 3 + -20 + 7h + 2h2 = 20 + -20 Combine like terms: 3 + -20 = -17 -17 + 7h + 2h2 = 20 + -20 Combine like terms: 20 + -20 = 0 -17 + 7h + 2h2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 3.5h + h2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 3.5h + 8.5 + h2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 3.5h + h2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 3.5h + h2 = 0 + 8.5 3.5h + h2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 3.5h + h2 = 8.5 The h term is 3.5h. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5h + 3.0625 + h2 = 8.5 + 3.0625 Reorder the terms: 3.0625 + 3.5h + h2 = 8.5 + 3.0625 Combine like terms: 8.5 + 3.0625 = 11.5625 3.0625 + 3.5h + h2 = 11.5625 Factor a perfect square on the left side: (h + 1.75)(h + 1.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (h + 1.75) equal to 3.400367627 and -3.400367627.Subproblem 1
h + 1.75 = 3.400367627 Simplifying h + 1.75 = 3.400367627 Reorder the terms: 1.75 + h = 3.400367627 Solving 1.75 + h = 3.400367627 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + h = 3.400367627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + h = 3.400367627 + -1.75 h = 3.400367627 + -1.75 Combine like terms: 3.400367627 + -1.75 = 1.650367627 h = 1.650367627 Simplifying h = 1.650367627Subproblem 2
h + 1.75 = -3.400367627 Simplifying h + 1.75 = -3.400367627 Reorder the terms: 1.75 + h = -3.400367627 Solving 1.75 + h = -3.400367627 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + h = -3.400367627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + h = -3.400367627 + -1.75 h = -3.400367627 + -1.75 Combine like terms: -3.400367627 + -1.75 = -5.150367627 h = -5.150367627 Simplifying h = -5.150367627Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.650367627, -5.150367627}
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