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Simplifying h2 + 12h = -19 Reorder the terms: 12h + h2 = -19 Solving 12h + h2 = -19 Solving for variable 'h'. Reorder the terms: 19 + 12h + h2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + 12h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 12h + -19 + h2 = 0 + -19 Reorder the terms: 19 + -19 + 12h + h2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 12h + h2 = 0 + -19 12h + h2 = 0 + -19 Combine like terms: 0 + -19 = -19 12h + h2 = -19 The h term is 12h. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12h + 36 + h2 = -19 + 36 Reorder the terms: 36 + 12h + h2 = -19 + 36 Combine like terms: -19 + 36 = 17 36 + 12h + h2 = 17 Factor a perfect square on the left side: (h + 6)(h + 6) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (h + 6) equal to 4.123105626 and -4.123105626.Subproblem 1
h + 6 = 4.123105626 Simplifying h + 6 = 4.123105626 Reorder the terms: 6 + h = 4.123105626 Solving 6 + h = 4.123105626 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + h = 4.123105626 + -6 Combine like terms: 6 + -6 = 0 0 + h = 4.123105626 + -6 h = 4.123105626 + -6 Combine like terms: 4.123105626 + -6 = -1.876894374 h = -1.876894374 Simplifying h = -1.876894374Subproblem 2
h + 6 = -4.123105626 Simplifying h + 6 = -4.123105626 Reorder the terms: 6 + h = -4.123105626 Solving 6 + h = -4.123105626 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + h = -4.123105626 + -6 Combine like terms: 6 + -6 = 0 0 + h = -4.123105626 + -6 h = -4.123105626 + -6 Combine like terms: -4.123105626 + -6 = -10.123105626 h = -10.123105626 Simplifying h = -10.123105626Solution
The solution to the problem is based on the solutions from the subproblems. h = {-1.876894374, -10.123105626}
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