Determine the next step for solving the quadratic equation by completing the square.

0 = –2x2 + 2x + 3
–3 = –2x2 + 2x
–3 = –2(x2 – x)
–3 + = –2(x2 – x + )
StartFraction negative 7 Over 2 EndFraction = –2(x – StartFraction 1 Over 2 EndFraction)2
StartFraction 7 Over 4 EndFraction = (x – StartFraction 1 Over 2 EndFraction)2
The two solutions are Plus or minus StartFraction StartRoot 7 EndRoot Over 2 EndFraction

-7/2 = -2(x-1/2)^2

Step-by-step explanation:

0 = –2x^2 + 2x + 3

Subtract 3 from each side

-3 = –2x^2 + 2x

Factor out the -2

-3 =- 2(x^2 -x)

Take the coefficient of x and divide by 2 and square it

-1 /2 = -1/2 ^2 = 1/4

Add it to each side  Remember the -2 on the outside so we need to multiply it by -2  

-2 *1/4 =  -1/2

-3 -1/2= -2(x^2 -x +1/4)

-7/2 = -2(x^2 -x +1/4)

-7/2 = -2(x-1/2)^2

A) StartFraction negative 7 Over 2 EndFraction = –2(x – StartFraction 1 Over 2 EndFraction)2

Step-by-step explanation:

–3 + = –2(x² – x + )

-3 + -2(½)² = -2(x² - 2(x)(½) + (½)²)

-3 - ½ = -2(x - ½)²

-7/2 = -2(x - ½)²

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: