How do you solve for x?

√(x + 3) = x - 3

√(x + 3) = x - 3

x + 3 = (x - 3)² {squared both sides}

x + 3 = (x - 3)(x - 3) {when you square a binomial, multiply it by itself}

x + 3 = x² - 6x + 9 {used foil method on right}

x² - 7x + 6 = 0 {subtracted x and subtracted 3 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}

If you put 1 back in, it doesn't check...it is an extraneous soultion

**x = 6**

*© Algebra House*