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Simplifying t2 + 18.37t + 30.6 = 0 Reorder the terms: 30.6 + 18.37t + t2 = 0 Solving 30.6 + 18.37t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-30.6' to each side of the equation. 30.6 + 18.37t + -30.6 + t2 = 0 + -30.6 Reorder the terms: 30.6 + -30.6 + 18.37t + t2 = 0 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + 18.37t + t2 = 0 + -30.6 18.37t + t2 = 0 + -30.6 Combine like terms: 0 + -30.6 = -30.6 18.37t + t2 = -30.6 The t term is 18.37t. Take half its coefficient (9.185). Square it (84.364225) and add it to both sides. Add '84.364225' to each side of the equation. 18.37t + 84.364225 + t2 = -30.6 + 84.364225 Reorder the terms: 84.364225 + 18.37t + t2 = -30.6 + 84.364225 Combine like terms: -30.6 + 84.364225 = 53.764225 84.364225 + 18.37t + t2 = 53.764225 Factor a perfect square on the left side: (t + 9.185)(t + 9.185) = 53.764225 Calculate the square root of the right side: 7.332409222 Break this problem into two subproblems by setting (t + 9.185) equal to 7.332409222 and -7.332409222.Subproblem 1
t + 9.185 = 7.332409222 Simplifying t + 9.185 = 7.332409222 Reorder the terms: 9.185 + t = 7.332409222 Solving 9.185 + t = 7.332409222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.185' to each side of the equation. 9.185 + -9.185 + t = 7.332409222 + -9.185 Combine like terms: 9.185 + -9.185 = 0.000 0.000 + t = 7.332409222 + -9.185 t = 7.332409222 + -9.185 Combine like terms: 7.332409222 + -9.185 = -1.852590778 t = -1.852590778 Simplifying t = -1.852590778Subproblem 2
t + 9.185 = -7.332409222 Simplifying t + 9.185 = -7.332409222 Reorder the terms: 9.185 + t = -7.332409222 Solving 9.185 + t = -7.332409222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.185' to each side of the equation. 9.185 + -9.185 + t = -7.332409222 + -9.185 Combine like terms: 9.185 + -9.185 = 0.000 0.000 + t = -7.332409222 + -9.185 t = -7.332409222 + -9.185 Combine like terms: -7.332409222 + -9.185 = -16.517409222 t = -16.517409222 Simplifying t = -16.517409222Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.852590778, -16.517409222}
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