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Simplifying (3t2) + 12t + -130 = 0 Reorder the terms: -130 + 12t + (3t2) = 0 Solving -130 + 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'. -43.33333333 + 4t + t2 = 0 Move the constant term to the right: Add '43.33333333' to each side of the equation. -43.33333333 + 4t + 43.33333333 + t2 = 0 + 43.33333333 Reorder the terms: -43.33333333 + 43.33333333 + 4t + t2 = 0 + 43.33333333 Combine like terms: -43.33333333 + 43.33333333 = 0.00000000 0.00000000 + 4t + t2 = 0 + 43.33333333 4t + t2 = 0 + 43.33333333 Combine like terms: 0 + 43.33333333 = 43.33333333 4t + t2 = 43.33333333 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 = 43.33333333 + 4 Reorder the terms: 4 + 4t + t2 = 43.33333333 + 4 Combine like terms: 43.33333333 + 4 = 47.33333333 4 + 4t + t2 = 47.33333333 Factor a perfect square on the left side: ((t) + 2)((t) + 2) = 47.33333333 Calculate the square root of the right side: 6.87992248 Break this problem into two subproblems by setting ((t) + 2) equal to 6.87992248 and -6.87992248.Subproblem 1
(t) + 2 = 6.87992248 Simplifying (t) + 2 = 6.87992248 t + 2 = 6.87992248 Reorder the terms: 2 + t = 6.87992248 Solving 2 + t = 6.87992248 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 = 6.87992248 + -2 Combine like terms: 2 + -2 = 0 0 + t = 6.87992248 + -2 t = 6.87992248 + -2 Combine like terms: 6.87992248 + -2 = 4.87992248 t = 4.87992248 Simplifying t = 4.87992248Subproblem 2
(t) + 2 = -6.87992248 Simplifying (t) + 2 = -6.87992248 t + 2 = -6.87992248 Reorder the terms: 2 + t = -6.87992248 Solving 2 + t = -6.87992248 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 = -6.87992248 + -2 Combine like terms: 2 + -2 = 0 0 + t = -6.87992248 + -2 t = -6.87992248 + -2 Combine like terms: -6.87992248 + -2 = -8.87992248 t = -8.87992248 Simplifying t = -8.87992248Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.87992248, -8.87992248}
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