What are the solutions to the quadratic equation x^2=7x+4

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