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Simplifying (4t + -1) + (t2 + -5) = 0 Reorder the terms: (-1 + 4t) + (t2 + -5) = 0 Remove parenthesis around (-1 + 4t) -1 + 4t + (t2 + -5) = 0 Reorder the terms: -1 + 4t + (-5 + t2) = 0 Remove parenthesis around (-5 + t2) -1 + 4t + -5 + t2 = 0 Reorder the terms: -1 + -5 + 4t + t2 = 0 Combine like terms: -1 + -5 = -6 -6 + 4t + t2 = 0 Solving -6 + 4t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 4t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4t + t2 = 0 + 6 4t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 4t + t2 = 6 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 = 6 + 4 Reorder the terms: 4 + 4t + t2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4t + t2 = 10 Factor a perfect square on the left side: (t + 2)(t + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
t + 2 = 3.16227766 Simplifying t + 2 = 3.16227766 Reorder the terms: 2 + t = 3.16227766 Solving 2 + t = 3.16227766 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 = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + t = 3.16227766 + -2 t = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 t = 1.16227766 Simplifying t = 1.16227766Subproblem 2
t + 2 = -3.16227766 Simplifying t + 2 = -3.16227766 Reorder the terms: 2 + t = -3.16227766 Solving 2 + t = -3.16227766 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 = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + t = -3.16227766 + -2 t = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 t = -5.16227766 Simplifying t = -5.16227766Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.16227766, -5.16227766}
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