Solving Quadratics ~ All Methods

Factoring

100

x^2-10x+21=0

x={3,7}

200

9x^2-25=0

x={-5/3,5/3}

300

3x^2-13x-30=0

x={-5/3,6}

400

3x^2=81-x^2

x={-9/2,9/2}

500

2x^2=x+21

x={-3,7/2}

Square Roots

100

5x^2-11=234

x=+-7

200

When is it best to use the square root method for solving quadratics?

When there is no 'b' term.

300

x^2-1=39

x=+-2sqrt10

400

4x^2-39=10

x=+-7/2

500

-2x^2-196=0

x=+-7isqrt2

Quadratic Formula

100

When can you use this method to solve a quadratic equation?

ALWAYS 

200

-2x^2+3x=4x-15

x={-3,5/2}

300

x^2-9=4x

x={2+-sqrt13}

400

-3x^2+8x-7=0

x={(4+-isqrt5)/3}

500

3x^2+x=-2x-7

x={-1/2+-(5isqrt3)/6}

Completing the Square

100

k^ 2 − 14k − 19 = 0

{7 + 2 sqrt17, 7 − 2 sqrt17}

200

x^ 2 − 20x + 64 = 0

{16, 4}

300

7n ^2 − 14n − 73 = 9

{ 7 + sqrt623/7 , 7 − sqrt623/ 7 }

400

3 p ^2 = −12p − 9

{−1, −3}

500

5n^ 2 + 19n = 3n + 92 − 3n^ 2

{ (−2 + 5 sqrt2)/ 2 , (−2 − 5sqrt 2)/ 2