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Simplifying 3t2 + 12t + -92 = 0 Reorder the terms: -92 + 12t + 3t2 = 0 Solving -92 + 12t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30.66666667 + 4t + t2 = 0 Move the constant term to the right: Add '30.66666667' to each side of the equation. -30.66666667 + 4t + 30.66666667 + t2 = 0 + 30.66666667 Reorder the terms: -30.66666667 + 30.66666667 + 4t + t2 = 0 + 30.66666667 Combine like terms: -30.66666667 + 30.66666667 = 0.00000000 0.00000000 + 4t + t2 = 0 + 30.66666667 4t + t2 = 0 + 30.66666667 Combine like terms: 0 + 30.66666667 = 30.66666667 4t + t2 = 30.66666667 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 30.66666667 + 4 Reorder the terms: 4 + 4t + t2 = 30.66666667 + 4 Combine like terms: 30.66666667 + 4 = 34.66666667 4 + 4t + t2 = 34.66666667 Factor a perfect square on the left side: (t + 2)(t + 2) = 34.66666667 Calculate the square root of the right side: 5.887840578 Break this problem into two subproblems by setting (t + 2) equal to 5.887840578 and -5.887840578.Subproblem 1
t + 2 = 5.887840578 Simplifying t + 2 = 5.887840578 Reorder the terms: 2 + t = 5.887840578 Solving 2 + t = 5.887840578 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 5.887840578 + -2 Combine like terms: 2 + -2 = 0 0 + t = 5.887840578 + -2 t = 5.887840578 + -2 Combine like terms: 5.887840578 + -2 = 3.887840578 t = 3.887840578 Simplifying t = 3.887840578Subproblem 2
t + 2 = -5.887840578 Simplifying t + 2 = -5.887840578 Reorder the terms: 2 + t = -5.887840578 Solving 2 + t = -5.887840578 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -5.887840578 + -2 Combine like terms: 2 + -2 = 0 0 + t = -5.887840578 + -2 t = -5.887840578 + -2 Combine like terms: -5.887840578 + -2 = -7.887840578 t = -7.887840578 Simplifying t = -7.887840578Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.887840578, -7.887840578}
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