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Simplifying t2 + 14t = -19 Reorder the terms: 14t + t2 = -19 Solving 14t + t2 = -19 Solving for variable 't'. Reorder the terms: 19 + 14t + t2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + 14t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 14t + -19 + t2 = 0 + -19 Reorder the terms: 19 + -19 + 14t + t2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 14t + t2 = 0 + -19 14t + t2 = 0 + -19 Combine like terms: 0 + -19 = -19 14t + t2 = -19 The t term is 14t. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14t + 49 + t2 = -19 + 49 Reorder the terms: 49 + 14t + t2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + 14t + t2 = 30 Factor a perfect square on the left side: (t + 7)(t + 7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (t + 7) equal to 5.477225575 and -5.477225575.Subproblem 1
t + 7 = 5.477225575 Simplifying t + 7 = 5.477225575 Reorder the terms: 7 + t = 5.477225575 Solving 7 + t = 5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = 5.477225575 + -7 Combine like terms: 7 + -7 = 0 0 + t = 5.477225575 + -7 t = 5.477225575 + -7 Combine like terms: 5.477225575 + -7 = -1.522774425 t = -1.522774425 Simplifying t = -1.522774425Subproblem 2
t + 7 = -5.477225575 Simplifying t + 7 = -5.477225575 Reorder the terms: 7 + t = -5.477225575 Solving 7 + t = -5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = -5.477225575 + -7 Combine like terms: 7 + -7 = 0 0 + t = -5.477225575 + -7 t = -5.477225575 + -7 Combine like terms: -5.477225575 + -7 = -12.477225575 t = -12.477225575 Simplifying t = -12.477225575Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.522774425, -12.477225575}
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