### Home > CCA2 > Chapter 12 > Lesson 12.1.3 > Problem 12-45

12-45.

Solve each equation. Check for extraneous solutions. Homework Help ✎

= *x*+ 1

Square both sides of the equation to remove the radical.

*x* + 7 = *x*^{2} + 2*x* + 1

Set the equation equal to 0 because it is quadratic (there is an *x*^{2}-term.)

0 = *x*^{2} + *x* − 6

Factor the polynomial.

Use the Zero Product Property to solve.

Check your solutions in the original equation. Do they both work?

Notice that you can factor *x*^{2} + 3*x* to *x*(*x* + 3).

Multiply both sides of the equation by a common denominator to remove the fractions.

2*x* − (*x* + 3) = −6

Solve for *x*.

*x* = −3

Substitute your solution back into the original equation. Is *x* = −3 a valid solution to this problem?