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Simplifying (-7t2 + 3t + -2) + (6t2 + 5t + 1) = 0 Reorder the terms: (-2 + 3t + -7t2) + (6t2 + 5t + 1) = 0 Remove parenthesis around (-2 + 3t + -7t2) -2 + 3t + -7t2 + (6t2 + 5t + 1) = 0 Reorder the terms: -2 + 3t + -7t2 + (1 + 5t + 6t2) = 0 Remove parenthesis around (1 + 5t + 6t2) -2 + 3t + -7t2 + 1 + 5t + 6t2 = 0 Reorder the terms: -2 + 1 + 3t + 5t + -7t2 + 6t2 = 0 Combine like terms: -2 + 1 = -1 -1 + 3t + 5t + -7t2 + 6t2 = 0 Combine like terms: 3t + 5t = 8t -1 + 8t + -7t2 + 6t2 = 0 Combine like terms: -7t2 + 6t2 = -1t2 -1 + 8t + -1t2 = 0 Solving -1 + 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'. 1 + -8t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -8t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8t + t2 = 0 + -1 -8t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8t + t2 = -1 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 = -1 + 16 Reorder the terms: 16 + -8t + t2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8t + t2 = 15 Factor a perfect square on the left side: (t + -4)(t + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (t + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
t + -4 = 3.872983346 Simplifying t + -4 = 3.872983346 Reorder the terms: -4 + t = 3.872983346 Solving -4 + t = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.872983346 + 4 t = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 t = 7.872983346 Simplifying t = 7.872983346Subproblem 2
t + -4 = -3.872983346 Simplifying t + -4 = -3.872983346 Reorder the terms: -4 + t = -3.872983346 Solving -4 + t = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.872983346 + 4 t = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 t = 0.127016654 Simplifying t = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.872983346, 0.127016654}
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