Solving Quadratic Equations with Real and Imaginary Solutions

Reorder the following steps for solving quadratics by square roots.

• REWRITE the equation as x² = n

• Take the SQUARE ROOT of both sides

• SIMPLIFY the radical. Place "±" to indicate both answers.

Solve the equation using the square roots method:

x² − 64 = 0

• x = ±8

• x = ±64

• x = ±32

• x = ±16

• x = ±4

Solve the equation using the square roots method:

7x² + 8 = 15

• x = ±1

• x = ±2

• x = ±3

• x = ±4

Solve the equation using the square roots method:

81x² + 5 = 21

What is the value of x?

• x = 2

• x = -2

• x = 1

• x = -1

Solve the equation using the square roots method:

8x² + 1 = 17

• x = ±2

• x = ±1

• x = ±3

• x = ±4

Solve the equation using the square roots method:

2x² − 9 = 55

• x = ±4

• x = ±5

• x = ±6

• x = ±7

Solve the equation using the square roots method:

9x² + 3 = 111

• x = ±4

• x = ±3

• x = ±2

Solve the equation using the square roots method

4 − 3x² = -77

• x = ±5

• x = ±3

• x = ±4

• x = ±6

Solve the equation using the square roots method:

5x² + 10 = 310

• x = ±6

• x = ±7

• x = ±5

• x = ±8

• x = ±20

• No Real Solution