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Simplifying 2h2 = 4h + 5 Reorder the terms: 2h2 = 5 + 4h Solving 2h2 = 5 + 4h Solving for variable 'h'. Reorder the terms: -5 + -4h + 2h2 = 5 + 4h + -5 + -4h Reorder the terms: -5 + -4h + 2h2 = 5 + -5 + 4h + -4h Combine like terms: 5 + -5 = 0 -5 + -4h + 2h2 = 0 + 4h + -4h -5 + -4h + 2h2 = 4h + -4h Combine like terms: 4h + -4h = 0 -5 + -4h + 2h2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -2h + h2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2h + 2.5 + h2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2h + h2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2h + h2 = 0 + 2.5 -2h + h2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2h + h2 = 2.5 The h term is -2h. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2h + 1 + h2 = 2.5 + 1 Reorder the terms: 1 + -2h + h2 = 2.5 + 1 Combine like terms: 2.5 + 1 = 3.5 1 + -2h + h2 = 3.5 Factor a perfect square on the left side: (h + -1)(h + -1) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (h + -1) equal to 1.870828693 and -1.870828693.Subproblem 1
h + -1 = 1.870828693 Simplifying h + -1 = 1.870828693 Reorder the terms: -1 + h = 1.870828693 Solving -1 + h = 1.870828693 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + h = 1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + h = 1.870828693 + 1 h = 1.870828693 + 1 Combine like terms: 1.870828693 + 1 = 2.870828693 h = 2.870828693 Simplifying h = 2.870828693Subproblem 2
h + -1 = -1.870828693 Simplifying h + -1 = -1.870828693 Reorder the terms: -1 + h = -1.870828693 Solving -1 + h = -1.870828693 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + h = -1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + h = -1.870828693 + 1 h = -1.870828693 + 1 Combine like terms: -1.870828693 + 1 = -0.870828693 h = -0.870828693 Simplifying h = -0.870828693Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.870828693, -0.870828693}
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