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Simplifying (-5t + 6) + -1(t2 + 3t + -1) = 0 Reorder the terms: (6 + -5t) + -1(t2 + 3t + -1) = 0 Remove parenthesis around (6 + -5t) 6 + -5t + -1(t2 + 3t + -1) = 0 Reorder the terms: 6 + -5t + -1(-1 + 3t + t2) = 0 6 + -5t + (-1 * -1 + 3t * -1 + t2 * -1) = 0 6 + -5t + (1 + -3t + -1t2) = 0 Reorder the terms: 6 + 1 + -5t + -3t + -1t2 = 0 Combine like terms: 6 + 1 = 7 7 + -5t + -3t + -1t2 = 0 Combine like terms: -5t + -3t = -8t 7 + -8t + -1t2 = 0 Solving 7 + -8t + -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'. -7 + 8t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 8t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + 8t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8t + t2 = 0 + 7 8t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 8t + t2 = 7 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 7 + 16 Reorder the terms: 16 + 8t + t2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8t + t2 = 23 Factor a perfect square on the left side: (t + 4)(t + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (t + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
t + 4 = 4.795831523 Simplifying t + 4 = 4.795831523 Reorder the terms: 4 + t = 4.795831523 Solving 4 + t = 4.795831523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + t = 4.795831523 + -4 t = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 t = 0.795831523 Simplifying t = 0.795831523Subproblem 2
t + 4 = -4.795831523 Simplifying t + 4 = -4.795831523 Reorder the terms: 4 + t = -4.795831523 Solving 4 + t = -4.795831523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + t = -4.795831523 + -4 t = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 t = -8.795831523 Simplifying t = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.795831523, -8.795831523}
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