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Simplifying 4t2 + -11t + -6 = 0 Reorder the terms: -6 + -11t + 4t2 = 0 Solving -6 + -11t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -2.75t + t2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.75t + 1.5 + t2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.75t + t2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.75t + t2 = 0 + 1.5 -2.75t + t2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.75t + t2 = 1.5 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 = 1.5 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = 1.5 + 1.890625 Combine like terms: 1.5 + 1.890625 = 3.390625 1.890625 + -2.75t + t2 = 3.390625 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (t + -1.375) equal to 1.841364983 and -1.841364983.Subproblem 1
t + -1.375 = 1.841364983 Simplifying t + -1.375 = 1.841364983 Reorder the terms: -1.375 + t = 1.841364983 Solving -1.375 + t = 1.841364983 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 = 1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 1.841364983 + 1.375 t = 1.841364983 + 1.375 Combine like terms: 1.841364983 + 1.375 = 3.216364983 t = 3.216364983 Simplifying t = 3.216364983Subproblem 2
t + -1.375 = -1.841364983 Simplifying t + -1.375 = -1.841364983 Reorder the terms: -1.375 + t = -1.841364983 Solving -1.375 + t = -1.841364983 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 = -1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -1.841364983 + 1.375 t = -1.841364983 + 1.375 Combine like terms: -1.841364983 + 1.375 = -0.466364983 t = -0.466364983 Simplifying t = -0.466364983Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.216364983, -0.466364983}
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