Answer:
x = 7/2 ±sqrt(65)/ 2
Step-by-step explanation:
x^2=7x+4
Subtract 7x from each side
x^2-7x=7x-7x+4
x^2 -7x =4
Complete the square
Take the coefficient of x and divide by 2
-7/2
Then square it
(-7/2)^2 = 49/4
Add this to each side
x^2 -7x +49/4 =4+49/4
(x-7/2)^2 = 4 +49/4
(x-7/2)^2 = 16/4 +49/4
(x-7/2)^2 =65/4
Take the square root of each side
sqrt((x-7/2)^2) =±sqrt(65/4)
x-7/2 = ±sqrt(65)/ sqrt(4)
x-7/2 = ±sqrt(65)/ 2
Add 7/2 to each side
x-7/2 +7/2=7/2 ±sqrt(65)/ 2
x = 7/2 ±sqrt(65)/ 2
