Solving Quadratic Equations

Solve by Square Root

100

These are solutions to the 

quadratic equation x² = 100.

NOTE: Name BOTH solutions!

What are  x = 10  and  x = -10?

200

These are solutions to the 

quadratic equation 7x² = 175.

NOTE: Name BOTH solutions!

What are  x = 5  and  x = -5?

300

These are solutions to the 

quadratic equation 4x² = 25.

NOTE: Name BOTH solutions!

What are  x = 5/2  and  x = -5/2?

[What are  x = 2.5 and x = -2.5?]

400

These are solutions to the 

quadratic equation 3x² - 2 = 46.

NOTE: Name BOTH solutions!

What are  x = 4  and  x = -4?

500

These are solutions to the 

quadratic equation 8x² - 7 = -1x² + 2.

NOTE: Name BOTH solutions!

What are  x = 1  and  x = -1?

Solve by Factoring (GCF)

100

These are solutions to the 

quadratic equation x² - 10x = 0.

NOTE: Name BOTH solutions!

What are  x = 0  and  x = 10?

200

These are solutions to the 

quadratic equation 25x² +10x = 0.

NOTE: Name BOTH solutions!

What are  x = 0  and  x = -2/5?

[What are  x = 0  and  x = -0.4?]

300

These are solutions to the 

quadratic equation 4x² = 20x.

NOTE: Name BOTH solutions!

What are  x = 0  and  x = -5?

400

These are solutions to the 

quadratic equation 15x² = 9x.

NOTE: Name BOTH solutions!

What are  x = 0  and  x = 3/5?

[What are  x = 0  and  x = 0.6?]

500

These are solutions to the 

quadratic equation 19x² + 2x = 3x² + 6x.

NOTE: Name BOTH solutions!

What are  x = 0  and  x = 1/4?

[What are  x = 0  and  x = 0.25?]

Solve by Factoring (1x^2 Trinomial)

100

These are the solutions to the equation

x² + 9x + 14 = 0.

HINT:  Name BOTH solutions!

What are  x = -2  and  x = -7?

200

These are the solutions to the equation

x² + 7x + 12 = 0.

HINT:  Name BOTH solutions!

What are  x = -3  and  x = -4?

300

These are the solutions to the equation

x² - 6x + 8 = 0.

HINT:  Name BOTH solutions!

What are  x = 2  and  x = 4?

400

These are the solutions to the equation

x² - 12x = -20.

HINT:  Name BOTH solutions!

What are  x = 2  and  x = 10?

500

These are the solutions to the equation

x² = 6x + 27.

HINT:  Name BOTH solutions!

What are  x = 9  and  x = -3?

Completing the Square

100

This value of c makes 

x² + 56x + c 

into a perfect square trinomial.

What is c = 784 ?

200

These are the solutions to the equation

(x - 9)² = 25.

HINT:  Name BOTH solutions!

What are  x = 14  and  x = 4?

300

This equation is equivalent to  

x² + 10x - 3 = 0, 

transformed into the form

(x + __)² = __.

What is (x + 5)² = 28 ?

400

These two features make a quadratic equation a good candidate for solving by completing the square.

What are, a leading term of 1x² 

and an even coefficient for x?

500

These are the solutions 

to the quadratic equation 

x² - 8x - 209 = 0.

HINT:  Solve by completing the square!

What are  x = 19  and  x = -11?

Quadratic Formula

100

THIS is the expression UNDER the square root sign in the quadratic formula.

What is  b² - 4ac ?

200

These values of a, b, and c would be used in the quadratic formula to solve the equation

10x² + 13x - 3 = 0.

What are,  a = 10,  b = 13,  and  c = -3.

300

These are the solutions to the quadratic equation

x² - 5x - 24 = 0.

HINT:  Solve by quadratic formula OR by factoring!

What are  x = -3  and  x = 8?

400

These are the solutions to the quadratic equation

x² - 14x - 72 = 0.

HINT:  Solve by quadratic formula OR by factoring!

What are  x = 18  and  x = -4 ?

500

These are the solutions to the quadratic equation

8x² + 18x - 81 = 0.

HINT:  Solve by quadratic formula OR by factoring!

What are  x = -4.5  and  x = 2.25?