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Simplifying -4.9H2 + 29.4H + 0 = 39.2 Reorder the terms: 0 + 29.4H + -4.9H2 = 39.2 Remove the zero: 29.4H + -4.9H2 = 39.2 Solving 29.4H + -4.9H2 = 39.2 Solving for variable 'H'. Reorder the terms: -39.2 + 29.4H + -4.9H2 = 39.2 + -39.2 Combine like terms: 39.2 + -39.2 = 0.0 -39.2 + 29.4H + -4.9H2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 8 + -6H + H2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6H + -8 + H2 = 0 + -8 Reorder the terms: 8 + -8 + -6H + H2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6H + H2 = 0 + -8 -6H + H2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6H + H2 = -8 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 = -8 + 9 Reorder the terms: 9 + -6H + H2 = -8 + 9 Combine like terms: -8 + 9 = 1 9 + -6H + H2 = 1 Factor a perfect square on the left side: (H + -3)(H + -3) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (H + -3) equal to 1 and -1.Subproblem 1
H + -3 = 1 Simplifying H + -3 = 1 Reorder the terms: -3 + H = 1 Solving -3 + H = 1 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 = 1 + 3 Combine like terms: -3 + 3 = 0 0 + H = 1 + 3 H = 1 + 3 Combine like terms: 1 + 3 = 4 H = 4 Simplifying H = 4Subproblem 2
H + -3 = -1 Simplifying H + -3 = -1 Reorder the terms: -3 + H = -1 Solving -3 + H = -1 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 = -1 + 3 Combine like terms: -3 + 3 = 0 0 + H = -1 + 3 H = -1 + 3 Combine like terms: -1 + 3 = 2 H = 2 Simplifying H = 2Solution
The solution to the problem is based on the solutions from the subproblems. H = {4, 2}
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