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Simplifying h2 + 14h + -26 = 0 Reorder the terms: -26 + 14h + h2 = 0 Solving -26 + 14h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 14h + 26 + h2 = 0 + 26 Reorder the terms: -26 + 26 + 14h + h2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 14h + h2 = 0 + 26 14h + h2 = 0 + 26 Combine like terms: 0 + 26 = 26 14h + h2 = 26 The h term is 14h. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14h + 49 + h2 = 26 + 49 Reorder the terms: 49 + 14h + h2 = 26 + 49 Combine like terms: 26 + 49 = 75 49 + 14h + h2 = 75 Factor a perfect square on the left side: (h + 7)(h + 7) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (h + 7) equal to 8.660254038 and -8.660254038.Subproblem 1
h + 7 = 8.660254038 Simplifying h + 7 = 8.660254038 Reorder the terms: 7 + h = 8.660254038 Solving 7 + h = 8.660254038 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = 8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + h = 8.660254038 + -7 h = 8.660254038 + -7 Combine like terms: 8.660254038 + -7 = 1.660254038 h = 1.660254038 Simplifying h = 1.660254038Subproblem 2
h + 7 = -8.660254038 Simplifying h + 7 = -8.660254038 Reorder the terms: 7 + h = -8.660254038 Solving 7 + h = -8.660254038 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = -8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + h = -8.660254038 + -7 h = -8.660254038 + -7 Combine like terms: -8.660254038 + -7 = -15.660254038 h = -15.660254038 Simplifying h = -15.660254038Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.660254038, -15.660254038}
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