### Home > CCA > Chapter 11 > Lesson 11.2.1 > Problem 11-33

11-33.

Find the real solutions to the equations below using any method of your choice. Homework Help ✎

2

*x*^{2}= 2 − 3*x*(2

*x*− 3)^{2}+ 4 = 0

Rewrite the equation in standard form.

2*x*^{2} + 3*x* = 2 − 3*x* + 3*x*

2*x*^{2} + 3*x* = 2

2*x*^{2} + 3*x* − 2 = 2 − 2

2*x*^{2} + 3*x* − 2 = 0

Solve by Zero Product Property:

Factor the equation:

2*x*^{2} + 3*x* − 2 = 0

(2*x* − 1)(*x* + 2) = 0

Get the roots from the factors.

(2*x* − 1) = 0*x* = 0.5

(*x* + 2) = 0*x* = −2

Solve by Quadratic Formula:

In the quadratic formula, substitute the coefficient of *x*^{2} for *a*, the coefficient of *x* for *b*, and the third term for *c*.

Simplify.

See the help for part (a).

This quadratic is not factorable. What happens when you use the other two methods? Are there any real solutions?