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Simplifying 66 = (h + 3) * 5h + 4 Reorder the terms: 66 = (3 + h) * 5h + 4 Reorder the terms for easier multiplication: 66 = 5h(3 + h) + 4 66 = (3 * 5h + h * 5h) + 4 66 = (15h + 5h2) + 4 Reorder the terms: 66 = 4 + 15h + 5h2 Solving 66 = 4 + 15h + 5h2 Solving for variable 'h'. Combine like terms: 66 + -4 = 62 62 + -15h + -5h2 = 4 + 15h + 5h2 + -4 + -15h + -5h2 Reorder the terms: 62 + -15h + -5h2 = 4 + -4 + 15h + -15h + 5h2 + -5h2 Combine like terms: 4 + -4 = 0 62 + -15h + -5h2 = 0 + 15h + -15h + 5h2 + -5h2 62 + -15h + -5h2 = 15h + -15h + 5h2 + -5h2 Combine like terms: 15h + -15h = 0 62 + -15h + -5h2 = 0 + 5h2 + -5h2 62 + -15h + -5h2 = 5h2 + -5h2 Combine like terms: 5h2 + -5h2 = 0 62 + -15h + -5h2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -12.4 + 3h + h2 = 0 Move the constant term to the right: Add '12.4' to each side of the equation. -12.4 + 3h + 12.4 + h2 = 0 + 12.4 Reorder the terms: -12.4 + 12.4 + 3h + h2 = 0 + 12.4 Combine like terms: -12.4 + 12.4 = 0.0 0.0 + 3h + h2 = 0 + 12.4 3h + h2 = 0 + 12.4 Combine like terms: 0 + 12.4 = 12.4 3h + h2 = 12.4 The h term is 3h. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3h + 2.25 + h2 = 12.4 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 12.4 + 2.25 Combine like terms: 12.4 + 2.25 = 14.65 2.25 + 3h + h2 = 14.65 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = 14.65 Calculate the square root of the right side: 3.827531842 Break this problem into two subproblems by setting (h + 1.5) equal to 3.827531842 and -3.827531842.Subproblem 1
h + 1.5 = 3.827531842 Simplifying h + 1.5 = 3.827531842 Reorder the terms: 1.5 + h = 3.827531842 Solving 1.5 + h = 3.827531842 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = 3.827531842 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 3.827531842 + -1.5 h = 3.827531842 + -1.5 Combine like terms: 3.827531842 + -1.5 = 2.327531842 h = 2.327531842 Simplifying h = 2.327531842Subproblem 2
h + 1.5 = -3.827531842 Simplifying h + 1.5 = -3.827531842 Reorder the terms: 1.5 + h = -3.827531842 Solving 1.5 + h = -3.827531842 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = -3.827531842 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -3.827531842 + -1.5 h = -3.827531842 + -1.5 Combine like terms: -3.827531842 + -1.5 = -5.327531842 h = -5.327531842 Simplifying h = -5.327531842Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.327531842, -5.327531842}
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