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Simplifying (4t + -1)(t + 5) = -21 Reorder the terms: (-1 + 4t)(t + 5) = -21 Reorder the terms: (-1 + 4t)(5 + t) = -21 Multiply (-1 + 4t) * (5 + t) (-1(5 + t) + 4t * (5 + t)) = -21 ((5 * -1 + t * -1) + 4t * (5 + t)) = -21 ((-5 + -1t) + 4t * (5 + t)) = -21 (-5 + -1t + (5 * 4t + t * 4t)) = -21 (-5 + -1t + (20t + 4t2)) = -21 Combine like terms: -1t + 20t = 19t (-5 + 19t + 4t2) = -21 Solving -5 + 19t + 4t2 = -21 Solving for variable 't'. Reorder the terms: -5 + 21 + 19t + 4t2 = -21 + 21 Combine like terms: -5 + 21 = 16 16 + 19t + 4t2 = -21 + 21 Combine like terms: -21 + 21 = 0 16 + 19t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + 4.75t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.75t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 4.75t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.75t + t2 = 0 + -4 4.75t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.75t + t2 = -4 The t term is 4.75t. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75t + 5.640625 + t2 = -4 + 5.640625 Reorder the terms: 5.640625 + 4.75t + t2 = -4 + 5.640625 Combine like terms: -4 + 5.640625 = 1.640625 5.640625 + 4.75t + t2 = 1.640625 Factor a perfect square on the left side: (t + 2.375)(t + 2.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (t + 2.375) equal to 1.280868846 and -1.280868846.Subproblem 1
t + 2.375 = 1.280868846 Simplifying t + 2.375 = 1.280868846 Reorder the terms: 2.375 + t = 1.280868846 Solving 2.375 + t = 1.280868846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = 1.280868846 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = 1.280868846 + -2.375 t = 1.280868846 + -2.375 Combine like terms: 1.280868846 + -2.375 = -1.094131154 t = -1.094131154 Simplifying t = -1.094131154Subproblem 2
t + 2.375 = -1.280868846 Simplifying t + 2.375 = -1.280868846 Reorder the terms: 2.375 + t = -1.280868846 Solving 2.375 + t = -1.280868846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = -1.280868846 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = -1.280868846 + -2.375 t = -1.280868846 + -2.375 Combine like terms: -1.280868846 + -2.375 = -3.655868846 t = -3.655868846 Simplifying t = -3.655868846Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.094131154, -3.655868846}
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