The Square Root Principle and Completing the Square Use the square root principle to solve quadratic equations. 2.Solve quadratic equations by completing the square.

Solve: Quadratic Equation Set = 0 Two solutions

The Square Root Principle If, then. Isolated perfect square. No middle term. Always 2 solutions.

Solve: 4∙ What do you see? Fractions Perfect square – no m term

Slide Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

Slide Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

Solve:

Solve:

Solve: 4∙7

2 rational solutions 2 irrational solutions 2 non-real imaginary solutions

Slide Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

Slide Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

Completing the Square ½ squared ½ ½ ½ Coefficient of the squared term must be1.

Solve: ½ + 5 squared irrational solutions Coefficient of squared term is 1.

Solve: ½ 3 2 squared irrational solutions Coefficient of squared term is NOT =

Solve: ½ squared 2 rational solutions Coefficient of squared term is NOT 1. Factorable!

Slide Copyright © 2011 Pearson Education, Inc. Solve by completing the square. a) b) c) d) 11.1

Slide Copyright © 2011 Pearson Education, Inc. Solve by completing the square. a) b) c) d) 11.1