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Simplifying 6t2 + -30t + 29 = 0 Reorder the terms: 29 + -30t + 6t2 = 0 Solving 29 + -30t + 6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.833333333 + -5t + t2 = 0 Move the constant term to the right: Add '-4.833333333' to each side of the equation. 4.833333333 + -5t + -4.833333333 + t2 = 0 + -4.833333333 Reorder the terms: 4.833333333 + -4.833333333 + -5t + t2 = 0 + -4.833333333 Combine like terms: 4.833333333 + -4.833333333 = 0.000000000 0.000000000 + -5t + t2 = 0 + -4.833333333 -5t + t2 = 0 + -4.833333333 Combine like terms: 0 + -4.833333333 = -4.833333333 -5t + t2 = -4.833333333 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -4.833333333 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -4.833333333 + 6.25 Combine like terms: -4.833333333 + 6.25 = 1.416666667 6.25 + -5t + t2 = 1.416666667 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 1.416666667 Calculate the square root of the right side: 1.190238072 Break this problem into two subproblems by setting (t + -2.5) equal to 1.190238072 and -1.190238072.Subproblem 1
t + -2.5 = 1.190238072 Simplifying t + -2.5 = 1.190238072 Reorder the terms: -2.5 + t = 1.190238072 Solving -2.5 + t = 1.190238072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 1.190238072 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.190238072 + 2.5 t = 1.190238072 + 2.5 Combine like terms: 1.190238072 + 2.5 = 3.690238072 t = 3.690238072 Simplifying t = 3.690238072Subproblem 2
t + -2.5 = -1.190238072 Simplifying t + -2.5 = -1.190238072 Reorder the terms: -2.5 + t = -1.190238072 Solving -2.5 + t = -1.190238072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -1.190238072 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.190238072 + 2.5 t = -1.190238072 + 2.5 Combine like terms: -1.190238072 + 2.5 = 1.309761928 t = 1.309761928 Simplifying t = 1.309761928Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.690238072, 1.309761928}
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