Solving Quadratic Equations

Solve by Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x² + 3x + 2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring. 15x² + x - 2 = 0

x =1/3  x = -2/5

500

Solve the following quadratic equation by factoring. 7x² - 19x = 6

x = 3 x = -2/7

Square Roots

100

Solve the following quadratic equation by using square roots: 7x² - 28 = 0

x = 2 or x = -2

200

Solve the following quadratic equation by using square roots: x² - 121 = 0

x = 11 x = -11

300

Solve the following quadratic equation by using square roots: 4x² +17 = 417

x = 10 or x = -10

400

Solve the following quadratic equation by using square roots: (x+4)² - 2 = 6

x = -4 +/- 2sqroot(2)

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 or x = -5

Completing the Square

100

Find the value of c that completes the square. x² + 22x + c

c = 121

200

State the value of c that completes the square. x² - 4x + c

c = 4

300

Solve by completing the square: x² - 8x +1 = 0

x = 4 +/- sqrt(15)

400

Solve the following quadratic equation by completing the square: x² - 2x - 35 = 0

x = -5 x = 7

500

Solve the following quadratic equation by completing the square: x² - 10x = 15

x = 5 +/- 2sqroot(10)

Quadratic Formula

100

Solve using the quadratic formula. Round your answer to the nearest hundredth. 5x² + 12x -2 = 0

x = 0.16 x = -2.56

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: 3x² + 4x = 1

x = (-2 +/- sqrt(7))/3

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 7 = x

No real solutions

500

Solve the following quadratic equation by using the quadratic formula: 9x² = 42x - 49

x = 7/3

Discriminant

100

Find the discriminant and state the number of solutions. 2x² + 5x - 6 = 0

Discriminant = 73 , Two Real Solutions

200

Find the discriminant and state the number of solutions. x² + 7x - 1 = 0

Discriminant = 53 , Two Real Solutions

300

Find the discriminant and state the number of solutions. 18x²+12x+2 = 0

Discriminant = 0 , One Real Solution

400

Find the discriminant and state the number of solutions. x² - 2x + 3 = 0

Discriminant = -8 , No Real Solutions

500

Find the discriminant and state the number of solutions. 12x + 9 = -4x²

Discriminant = 0 , One Real Solution