(3x + 7)^1/2 = x - 1

3x + 7 = (x - 1)² {squared both sides to eliminate the square root sign}

3x + 7 = (x - 1)(x - 1) {to square a binomial, multiply it by itself}

3x + 7 = x² - 2x + 1 {used foil method}

x² - 5x - 6 = 0 {subtracted 3x and 7 from both sides}

(x - 6)(x + 1) = 0 {factored into two binomials}

x - 6 = 0 or x + 1 = 0 {set each factor equal to 0}

x = 6 or x = -1 {solved each equation for x}

**x = 6**

-1 is an "extraneous solution". If you substitute -1 back in for x, it does not make a true statement. Therefore, it is an "extraneous solution".

*© Algebra House*