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Simplifying h2 + 6h + 4 = 0 Reorder the terms: 4 + 6h + h2 = 0 Solving 4 + 6h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6h + -4 + h2 = 0 + -4 Reorder the terms: 4 + -4 + 6h + h2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6h + h2 = 0 + -4 6h + h2 = 0 + -4 Combine like terms: 0 + -4 = -4 6h + h2 = -4 The h term is 6h. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6h + 9 + h2 = -4 + 9 Reorder the terms: 9 + 6h + h2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6h + h2 = 5 Factor a perfect square on the left side: (h + 3)(h + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (h + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
h + 3 = 2.236067978 Simplifying h + 3 = 2.236067978 Reorder the terms: 3 + h = 2.236067978 Solving 3 + h = 2.236067978 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + h = 2.236067978 + -3 h = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 h = -0.763932022 Simplifying h = -0.763932022Subproblem 2
h + 3 = -2.236067978 Simplifying h + 3 = -2.236067978 Reorder the terms: 3 + h = -2.236067978 Solving 3 + h = -2.236067978 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + h = -2.236067978 + -3 h = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 h = -5.236067978 Simplifying h = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.763932022, -5.236067978}
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