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Simplifying h2 + 7h + 2 = 0 Reorder the terms: 2 + 7h + h2 = 0 Solving 2 + 7h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7h + -2 + h2 = 0 + -2 Reorder the terms: 2 + -2 + 7h + h2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7h + h2 = 0 + -2 7h + h2 = 0 + -2 Combine like terms: 0 + -2 = -2 7h + h2 = -2 The h term is 7h. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7h + 12.25 + h2 = -2 + 12.25 Reorder the terms: 12.25 + 7h + h2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + 7h + h2 = 10.25 Factor a perfect square on the left side: (h + 3.5)(h + 3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (h + 3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
h + 3.5 = 3.201562119 Simplifying h + 3.5 = 3.201562119 Reorder the terms: 3.5 + h = 3.201562119 Solving 3.5 + h = 3.201562119 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 3.201562119 + -3.5 h = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 h = -0.298437881 Simplifying h = -0.298437881Subproblem 2
h + 3.5 = -3.201562119 Simplifying h + 3.5 = -3.201562119 Reorder the terms: 3.5 + h = -3.201562119 Solving 3.5 + h = -3.201562119 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -3.201562119 + -3.5 h = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 h = -6.701562119 Simplifying h = -6.701562119Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.298437881, -6.701562119}
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