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Simplifying 2H2 + -20 = H + 4H + -4 Reorder the terms: -20 + 2H2 = H + 4H + -4 Reorder the terms: -20 + 2H2 = -4 + H + 4H Combine like terms: H + 4H = 5H -20 + 2H2 = -4 + 5H Solving -20 + 2H2 = -4 + 5H Solving for variable 'H'. Reorder the terms: -20 + 4 + -5H + 2H2 = -4 + 5H + 4 + -5H Combine like terms: -20 + 4 = -16 -16 + -5H + 2H2 = -4 + 5H + 4 + -5H Reorder the terms: -16 + -5H + 2H2 = -4 + 4 + 5H + -5H Combine like terms: -4 + 4 = 0 -16 + -5H + 2H2 = 0 + 5H + -5H -16 + -5H + 2H2 = 5H + -5H Combine like terms: 5H + -5H = 0 -16 + -5H + 2H2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -2.5H + H2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2.5H + 8 + H2 = 0 + 8 Reorder the terms: -8 + 8 + -2.5H + H2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2.5H + H2 = 0 + 8 -2.5H + H2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2.5H + H2 = 8 The H term is -2.5H. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5H + 1.5625 + H2 = 8 + 1.5625 Reorder the terms: 1.5625 + -2.5H + H2 = 8 + 1.5625 Combine like terms: 8 + 1.5625 = 9.5625 1.5625 + -2.5H + H2 = 9.5625 Factor a perfect square on the left side: (H + -1.25)(H + -1.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (H + -1.25) equal to 3.092329219 and -3.092329219.Subproblem 1
H + -1.25 = 3.092329219 Simplifying H + -1.25 = 3.092329219 Reorder the terms: -1.25 + H = 3.092329219 Solving -1.25 + H = 3.092329219 Solving for variable 'H'. Move all terms containing H to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + H = 3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + H = 3.092329219 + 1.25 H = 3.092329219 + 1.25 Combine like terms: 3.092329219 + 1.25 = 4.342329219 H = 4.342329219 Simplifying H = 4.342329219Subproblem 2
H + -1.25 = -3.092329219 Simplifying H + -1.25 = -3.092329219 Reorder the terms: -1.25 + H = -3.092329219 Solving -1.25 + H = -3.092329219 Solving for variable 'H'. Move all terms containing H to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + H = -3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + H = -3.092329219 + 1.25 H = -3.092329219 + 1.25 Combine like terms: -3.092329219 + 1.25 = -1.842329219 H = -1.842329219 Simplifying H = -1.842329219Solution
The solution to the problem is based on the solutions from the subproblems. H = {4.342329219, -1.842329219}
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