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Simplifying 1.8 + -3h = h2 Solving 1.8 + -3h = h2 Solving for variable 'h'. Combine like terms: h2 + -1h2 = 0 1.8 + -3h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1.8 + 3h + h2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 3h + 1.8 + h2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 3h + h2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 3h + h2 = 0 + 1.8 3h + h2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 3h + h2 = 1.8 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 = 1.8 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 1.8 + 2.25 Combine like terms: 1.8 + 2.25 = 4.05 2.25 + 3h + h2 = 4.05 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = 4.05 Calculate the square root of the right side: 2.01246118 Break this problem into two subproblems by setting (h + 1.5) equal to 2.01246118 and -2.01246118.Subproblem 1
h + 1.5 = 2.01246118 Simplifying h + 1.5 = 2.01246118 Reorder the terms: 1.5 + h = 2.01246118 Solving 1.5 + h = 2.01246118 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 = 2.01246118 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 2.01246118 + -1.5 h = 2.01246118 + -1.5 Combine like terms: 2.01246118 + -1.5 = 0.51246118 h = 0.51246118 Simplifying h = 0.51246118Subproblem 2
h + 1.5 = -2.01246118 Simplifying h + 1.5 = -2.01246118 Reorder the terms: 1.5 + h = -2.01246118 Solving 1.5 + h = -2.01246118 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 = -2.01246118 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -2.01246118 + -1.5 h = -2.01246118 + -1.5 Combine like terms: -2.01246118 + -1.5 = -3.51246118 h = -3.51246118 Simplifying h = -3.51246118Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.51246118, -3.51246118}
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