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Simplifying 4t2 + 11t = 12 Reorder the terms: 11t + 4t2 = 12 Solving 11t + 4t2 = 12 Solving for variable 't'. Reorder the terms: -12 + 11t + 4t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 2.75t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.75t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 2.75t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.75t + t2 = 0 + 3 2.75t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.75t + t2 = 3 The t term is 2.75t. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75t + 1.890625 + t2 = 3 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = 3 + 1.890625 Combine like terms: 3 + 1.890625 = 4.890625 1.890625 + 2.75t + t2 = 4.890625 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (t + 1.375) equal to 2.211475752 and -2.211475752.Subproblem 1
t + 1.375 = 2.211475752 Simplifying t + 1.375 = 2.211475752 Reorder the terms: 1.375 + t = 2.211475752 Solving 1.375 + t = 2.211475752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = 2.211475752 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = 2.211475752 + -1.375 t = 2.211475752 + -1.375 Combine like terms: 2.211475752 + -1.375 = 0.836475752 t = 0.836475752 Simplifying t = 0.836475752Subproblem 2
t + 1.375 = -2.211475752 Simplifying t + 1.375 = -2.211475752 Reorder the terms: 1.375 + t = -2.211475752 Solving 1.375 + t = -2.211475752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = -2.211475752 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = -2.211475752 + -1.375 t = -2.211475752 + -1.375 Combine like terms: -2.211475752 + -1.375 = -3.586475752 t = -3.586475752 Simplifying t = -3.586475752Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.836475752, -3.586475752}
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