Answer:
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 - ½)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
7/2 = -2(x - ½)²
