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Simplifying t2 + -12t = -19 Reorder the terms: -12t + t2 = -19 Solving -12t + t2 = -19 Solving for variable 't'. Reorder the terms: 19 + -12t + t2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -12t + -19 + t2 = 0 + -19 Reorder the terms: 19 + -19 + -12t + t2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -12t + t2 = 0 + -19 -12t + t2 = 0 + -19 Combine like terms: 0 + -19 = -19 -12t + t2 = -19 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -19 + 36 Reorder the terms: 36 + -12t + t2 = -19 + 36 Combine like terms: -19 + 36 = 17 36 + -12t + t2 = 17 Factor a perfect square on the left side: (t + -6)(t + -6) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (t + -6) equal to 4.123105626 and -4.123105626.Subproblem 1
t + -6 = 4.123105626 Simplifying t + -6 = 4.123105626 Reorder the terms: -6 + t = 4.123105626 Solving -6 + t = 4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + t = 4.123105626 + 6 t = 4.123105626 + 6 Combine like terms: 4.123105626 + 6 = 10.123105626 t = 10.123105626 Simplifying t = 10.123105626Subproblem 2
t + -6 = -4.123105626 Simplifying t + -6 = -4.123105626 Reorder the terms: -6 + t = -4.123105626 Solving -6 + t = -4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + t = -4.123105626 + 6 t = -4.123105626 + 6 Combine like terms: -4.123105626 + 6 = 1.876894374 t = 1.876894374 Simplifying t = 1.876894374Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.123105626, 1.876894374}
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