Solving Quadractic Equations

Square Root

100

7x^2=112

x={-4,4}

200

X^2+65=90

X={-5,5}

300

8x^2-40/4=470

x={-4√ 15,4√ 15}

400

-3x^2+4=-104

x={-6,6}

500

3x^2-8+56

X=8/√ 3

Completing the square

100

X^2+4x=5

X={-5,1}

200

t^2-20t=2

t={10±√102}

300

x^2+4x-16=0

x={-2±2√5}

400

m^2+16m=-59

-8± √5

500

2x^2+20x+8=0

x=−5-√29  and x=−5+√ 29

Factoring

100

X^2+14x+49

(X+7)^2

200

5x^2+12x+4

(3x+2)^2

300

X^2-3x-10

(x+2)(x-5)

400

-X^2+10x^2+24x

(-x+2) (x+2)

500

3x^2-10x-8

(3x+2) (x-4)

Quadratic Formula

100

2x^2+5x-1=0

-5 +√33/4 and -5-√33/4 

200

x²-7=4x

x={-1.32,5.32}

300

x²-4x+1=0

x=4±√12/2

400

3x²-7x-6=0

x={-2/3,3}

500

2x²+4x-7=0

x=-2±3√2/2

Completing the square with vertex form

100

y=x²-8x+11

y=(x-4)²-5

Vertex= (4,-5)

200

y= -x²-8x-7

y= (x+4)²-9

Vertex=(-4,-9)

300

y=x²-2x+3

y= (x-1)²+2

Vertex= (1,2)

400

y= 2x²-20x+36

y= (x-5)+7

Vertex= (5,-7)

500

y= -x²-8x-7

y= (x+4)²-9

Vertex= (-4,9)