Solve the equation by identifying the quadratic form Use a s

Solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. (Enter your answers as a comma-separated list.)

Solution

3(t - 1)² - 22(t - 1) = -7

or, 3(t - 1)² - 22(t - 1) + 7 = 0

or,  3(t - 1)² - 21(t - 1) - (t - 1) + 7 = 0

or, 3(t - 1)[(t - 1) - 7] - [(t - 1) - 7] = 0

or, [(t - 1) - 7][3(t - 1) - 1] = 0

or, (t - 1) - 7 = 0 and 3(t - 1) - 1 = 0

or, t = 1 + 7 and, 3t - 3 - 1 = 0

or, t = 8, 4/3

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