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Simplifying (6 + -1t) + (7 + -1t)(-4 + -1t) = 0 Remove parenthesis around (6 + -1t) 6 + -1t + (7 + -1t)(-4 + -1t) = 0 Multiply (7 + -1t) * (-4 + -1t) 6 + -1t + (7(-4 + -1t) + -1t * (-4 + -1t)) = 0 6 + -1t + ((-4 * 7 + -1t * 7) + -1t * (-4 + -1t)) = 0 6 + -1t + ((-28 + -7t) + -1t * (-4 + -1t)) = 0 6 + -1t + (-28 + -7t + (-4 * -1t + -1t * -1t)) = 0 6 + -1t + (-28 + -7t + (4t + 1t2)) = 0 Combine like terms: -7t + 4t = -3t 6 + -1t + (-28 + -3t + 1t2) = 0 Reorder the terms: 6 + -28 + -1t + -3t + 1t2 = 0 Combine like terms: 6 + -28 = -22 -22 + -1t + -3t + 1t2 = 0 Combine like terms: -1t + -3t = -4t -22 + -4t + 1t2 = 0 Solving -22 + -4t + 1t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -4t + 22 + t2 = 0 + 22 Reorder the terms: -22 + 22 + -4t + t2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -4t + t2 = 0 + 22 -4t + t2 = 0 + 22 Combine like terms: 0 + 22 = 22 -4t + t2 = 22 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 22 + 4 Reorder the terms: 4 + -4t + t2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + -4t + t2 = 26 Factor a perfect square on the left side: (t + -2)(t + -2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + -2) equal to 5.099019514 and -5.099019514.Subproblem 1
t + -2 = 5.099019514 Simplifying t + -2 = 5.099019514 Reorder the terms: -2 + t = 5.099019514 Solving -2 + t = 5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + t = 5.099019514 + 2 t = 5.099019514 + 2 Combine like terms: 5.099019514 + 2 = 7.099019514 t = 7.099019514 Simplifying t = 7.099019514Subproblem 2
t + -2 = -5.099019514 Simplifying t + -2 = -5.099019514 Reorder the terms: -2 + t = -5.099019514 Solving -2 + t = -5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + t = -5.099019514 + 2 t = -5.099019514 + 2 Combine like terms: -5.099019514 + 2 = -3.099019514 t = -3.099019514 Simplifying t = -3.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.099019514, -3.099019514}
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