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Simplifying 0 = -1t2 + 2t + 7 Reorder the terms: 0 = 7 + 2t + -1t2 Solving 0 = 7 + 2t + -1t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + -2t + t2 = 7 + 2t + -1t2 + -7 + -2t + t2 Reorder the terms: -7 + -2t + t2 = 7 + -7 + 2t + -2t + -1t2 + t2 Combine like terms: 7 + -7 = 0 -7 + -2t + t2 = 0 + 2t + -2t + -1t2 + t2 -7 + -2t + t2 = 2t + -2t + -1t2 + t2 Combine like terms: 2t + -2t = 0 -7 + -2t + t2 = 0 + -1t2 + t2 -7 + -2t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -7 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + -2t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2t + t2 = 0 + 7 -2t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2t + t2 = 7 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 7 + 1 Reorder the terms: 1 + -2t + t2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2t + t2 = 8 Factor a perfect square on the left side: (t + -1)(t + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (t + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
t + -1 = 2.828427125 Simplifying t + -1 = 2.828427125 Reorder the terms: -1 + t = 2.828427125 Solving -1 + t = 2.828427125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + t = 2.828427125 + 1 t = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 t = 3.828427125 Simplifying t = 3.828427125Subproblem 2
t + -1 = -2.828427125 Simplifying t + -1 = -2.828427125 Reorder the terms: -1 + t = -2.828427125 Solving -1 + t = -2.828427125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + t = -2.828427125 + 1 t = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 t = -1.828427125 Simplifying t = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.828427125, -1.828427125}
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