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

11-33.
  1. Find the real solutions to the equations below using any method of your choice. Homework Help ✎

    1. 2x2 = 2 − 3x

    2. (2x − 3)2 + 4 = 0

Rewrite the equation in standard form.
2x2 + 3x = 2 − 3x + 3x
2x2 + 3x = 2
2x2 + 3x − 2 = 2 − 2
2x2 + 3x − 2 = 0

Solve by Zero Product Property:

Factor the equation:
2x2 + 3x − 2 = 0
(2x − 1)(x + 2) = 0

Get the roots from the factors.
(2x − 1) = 0
x = 0.5

(x + 2) = 0
x = −2

Solve by Quadratic Formula:

In the quadratic formula, substitute the coefficient of x2 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?