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Simplifying 7t2 + -9t + -8 = 0 Reorder the terms: -8 + -9t + 7t2 = 0 Solving -8 + -9t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -1.285714286t + t2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1.285714286t + 1.142857143 + t2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1.285714286t + t2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1.285714286t + t2 = 0 + 1.142857143 -1.285714286t + t2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1.285714286t + t2 = 1.142857143 The t term is -1.285714286t. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286t + 0.4132653063 + t2 = 1.142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286t + t2 = 1.142857143 + 0.4132653063 Combine like terms: 1.142857143 + 0.4132653063 = 1.5561224493 0.4132653063 + -1.285714286t + t2 = 1.5561224493 Factor a perfect square on the left side: (t + -0.642857143)(t + -0.642857143) = 1.5561224493 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (t + -0.642857143) equal to 1.247446371 and -1.247446371.Subproblem 1
t + -0.642857143 = 1.247446371 Simplifying t + -0.642857143 = 1.247446371 Reorder the terms: -0.642857143 + t = 1.247446371 Solving -0.642857143 + t = 1.247446371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + t = 1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + t = 1.247446371 + 0.642857143 t = 1.247446371 + 0.642857143 Combine like terms: 1.247446371 + 0.642857143 = 1.890303514 t = 1.890303514 Simplifying t = 1.890303514Subproblem 2
t + -0.642857143 = -1.247446371 Simplifying t + -0.642857143 = -1.247446371 Reorder the terms: -0.642857143 + t = -1.247446371 Solving -0.642857143 + t = -1.247446371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + t = -1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + t = -1.247446371 + 0.642857143 t = -1.247446371 + 0.642857143 Combine like terms: -1.247446371 + 0.642857143 = -0.604589228 t = -0.604589228 Simplifying t = -0.604589228Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.890303514, -0.604589228}
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