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Simplifying h2 + 4h + 4 = 37 Reorder the terms: 4 + 4h + h2 = 37 Solving 4 + 4h + h2 = 37 Solving for variable 'h'. Reorder the terms: 4 + -37 + 4h + h2 = 37 + -37 Combine like terms: 4 + -37 = -33 -33 + 4h + h2 = 37 + -37 Combine like terms: 37 + -37 = 0 -33 + 4h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 4h + 33 + h2 = 0 + 33 Reorder the terms: -33 + 33 + 4h + h2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4h + h2 = 0 + 33 4h + h2 = 0 + 33 Combine like terms: 0 + 33 = 33 4h + h2 = 33 The h term is 4h. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4h + 4 + h2 = 33 + 4 Reorder the terms: 4 + 4h + h2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4h + h2 = 37 Factor a perfect square on the left side: (h + 2)(h + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (h + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
h + 2 = 6.08276253 Simplifying h + 2 = 6.08276253 Reorder the terms: 2 + h = 6.08276253 Solving 2 + h = 6.08276253 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + h = 6.08276253 + -2 h = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 h = 4.08276253 Simplifying h = 4.08276253Subproblem 2
h + 2 = -6.08276253 Simplifying h + 2 = -6.08276253 Reorder the terms: 2 + h = -6.08276253 Solving 2 + h = -6.08276253 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + h = -6.08276253 + -2 h = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 h = -8.08276253 Simplifying h = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.08276253, -8.08276253}
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