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Simplifying h2 + 14h = 9 Reorder the terms: 14h + h2 = 9 Solving 14h + h2 = 9 Solving for variable 'h'. Reorder the terms: -9 + 14h + h2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 14h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 14h + 9 + h2 = 0 + 9 Reorder the terms: -9 + 9 + 14h + h2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 14h + h2 = 0 + 9 14h + h2 = 0 + 9 Combine like terms: 0 + 9 = 9 14h + h2 = 9 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 = 9 + 49 Reorder the terms: 49 + 14h + h2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + 14h + h2 = 58 Factor a perfect square on the left side: (h + 7)(h + 7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (h + 7) equal to 7.615773106 and -7.615773106.Subproblem 1
h + 7 = 7.615773106 Simplifying h + 7 = 7.615773106 Reorder the terms: 7 + h = 7.615773106 Solving 7 + h = 7.615773106 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 = 7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + h = 7.615773106 + -7 h = 7.615773106 + -7 Combine like terms: 7.615773106 + -7 = 0.615773106 h = 0.615773106 Simplifying h = 0.615773106Subproblem 2
h + 7 = -7.615773106 Simplifying h + 7 = -7.615773106 Reorder the terms: 7 + h = -7.615773106 Solving 7 + h = -7.615773106 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 = -7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + h = -7.615773106 + -7 h = -7.615773106 + -7 Combine like terms: -7.615773106 + -7 = -14.615773106 h = -14.615773106 Simplifying h = -14.615773106Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.615773106, -14.615773106}
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