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Simplifying 2H2 + -20 = H + 4(H + -4) Reorder the terms: -20 + 2H2 = H + 4(H + -4) Reorder the terms: -20 + 2H2 = H + 4(-4 + H) -20 + 2H2 = H + (-4 * 4 + H * 4) -20 + 2H2 = H + (-16 + 4H) Reorder the terms: -20 + 2H2 = -16 + H + 4H Combine like terms: H + 4H = 5H -20 + 2H2 = -16 + 5H Solving -20 + 2H2 = -16 + 5H Solving for variable 'H'. Reorder the terms: -20 + 16 + -5H + 2H2 = -16 + 5H + 16 + -5H Combine like terms: -20 + 16 = -4 -4 + -5H + 2H2 = -16 + 5H + 16 + -5H Reorder the terms: -4 + -5H + 2H2 = -16 + 16 + 5H + -5H Combine like terms: -16 + 16 = 0 -4 + -5H + 2H2 = 0 + 5H + -5H -4 + -5H + 2H2 = 5H + -5H Combine like terms: 5H + -5H = 0 -4 + -5H + 2H2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -2.5H + H2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.5H + 2 + H2 = 0 + 2 Reorder the terms: -2 + 2 + -2.5H + H2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.5H + H2 = 0 + 2 -2.5H + H2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.5H + H2 = 2 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 = 2 + 1.5625 Reorder the terms: 1.5625 + -2.5H + H2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + -2.5H + H2 = 3.5625 Factor a perfect square on the left side: (H + -1.25)(H + -1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (H + -1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
H + -1.25 = 1.887458609 Simplifying H + -1.25 = 1.887458609 Reorder the terms: -1.25 + H = 1.887458609 Solving -1.25 + H = 1.887458609 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 = 1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + H = 1.887458609 + 1.25 H = 1.887458609 + 1.25 Combine like terms: 1.887458609 + 1.25 = 3.137458609 H = 3.137458609 Simplifying H = 3.137458609Subproblem 2
H + -1.25 = -1.887458609 Simplifying H + -1.25 = -1.887458609 Reorder the terms: -1.25 + H = -1.887458609 Solving -1.25 + H = -1.887458609 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 = -1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + H = -1.887458609 + 1.25 H = -1.887458609 + 1.25 Combine like terms: -1.887458609 + 1.25 = -0.637458609 H = -0.637458609 Simplifying H = -0.637458609Solution
The solution to the problem is based on the solutions from the subproblems. H = {3.137458609, -0.637458609}
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