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Simplifying 32 + 12t + -1t2 = 0 Solving 32 + 12t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + -12t + t2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -12t + 32 + t2 = 0 + 32 Reorder the terms: -32 + 32 + -12t + t2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -12t + t2 = 0 + 32 -12t + t2 = 0 + 32 Combine like terms: 0 + 32 = 32 -12t + t2 = 32 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 32 + 36 Reorder the terms: 36 + -12t + t2 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + -12t + t2 = 68 Factor a perfect square on the left side: (t + -6)(t + -6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (t + -6) equal to 8.246211251 and -8.246211251.Subproblem 1
t + -6 = 8.246211251 Simplifying t + -6 = 8.246211251 Reorder the terms: -6 + t = 8.246211251 Solving -6 + t = 8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + t = 8.246211251 + 6 t = 8.246211251 + 6 Combine like terms: 8.246211251 + 6 = 14.246211251 t = 14.246211251 Simplifying t = 14.246211251Subproblem 2
t + -6 = -8.246211251 Simplifying t + -6 = -8.246211251 Reorder the terms: -6 + t = -8.246211251 Solving -6 + t = -8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + t = -8.246211251 + 6 t = -8.246211251 + 6 Combine like terms: -8.246211251 + 6 = -2.246211251 t = -2.246211251 Simplifying t = -2.246211251Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.246211251, -2.246211251}
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