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Simplifying h2 + 44h + -6279 = 0 Reorder the terms: -6279 + 44h + h2 = 0 Solving -6279 + 44h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '6279' to each side of the equation. -6279 + 44h + 6279 + h2 = 0 + 6279 Reorder the terms: -6279 + 6279 + 44h + h2 = 0 + 6279 Combine like terms: -6279 + 6279 = 0 0 + 44h + h2 = 0 + 6279 44h + h2 = 0 + 6279 Combine like terms: 0 + 6279 = 6279 44h + h2 = 6279 The h term is 44h. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44h + 484 + h2 = 6279 + 484 Reorder the terms: 484 + 44h + h2 = 6279 + 484 Combine like terms: 6279 + 484 = 6763 484 + 44h + h2 = 6763 Factor a perfect square on the left side: (h + 22)(h + 22) = 6763 Calculate the square root of the right side: 82.23746105 Break this problem into two subproblems by setting (h + 22) equal to 82.23746105 and -82.23746105.Subproblem 1
h + 22 = 82.23746105 Simplifying h + 22 = 82.23746105 Reorder the terms: 22 + h = 82.23746105 Solving 22 + h = 82.23746105 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + h = 82.23746105 + -22 Combine like terms: 22 + -22 = 0 0 + h = 82.23746105 + -22 h = 82.23746105 + -22 Combine like terms: 82.23746105 + -22 = 60.23746105 h = 60.23746105 Simplifying h = 60.23746105Subproblem 2
h + 22 = -82.23746105 Simplifying h + 22 = -82.23746105 Reorder the terms: 22 + h = -82.23746105 Solving 22 + h = -82.23746105 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + h = -82.23746105 + -22 Combine like terms: 22 + -22 = 0 0 + h = -82.23746105 + -22 h = -82.23746105 + -22 Combine like terms: -82.23746105 + -22 = -104.23746105 h = -104.23746105 Simplifying h = -104.23746105Solution
The solution to the problem is based on the solutions from the subproblems. h = {60.23746105, -104.23746105}
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