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Simplifying t2 + -4t + -13 = 0 Reorder the terms: -13 + -4t + t2 = 0 Solving -13 + -4t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4t + 13 + t2 = 0 + 13 Reorder the terms: -13 + 13 + -4t + t2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4t + t2 = 0 + 13 -4t + t2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4t + t2 = 13 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 = 13 + 4 Reorder the terms: 4 + -4t + t2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4t + t2 = 17 Factor a perfect square on the left side: (t + -2)(t + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (t + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
t + -2 = 4.123105626 Simplifying t + -2 = 4.123105626 Reorder the terms: -2 + t = 4.123105626 Solving -2 + t = 4.123105626 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 = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.123105626 + 2 t = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 t = 6.123105626 Simplifying t = 6.123105626Subproblem 2
t + -2 = -4.123105626 Simplifying t + -2 = -4.123105626 Reorder the terms: -2 + t = -4.123105626 Solving -2 + t = -4.123105626 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 = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.123105626 + 2 t = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 t = -2.123105626 Simplifying t = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.123105626, -2.123105626}
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