X^2+3x=7/4

Solve the equation by completing the square

Note that

(x + a) ^2 = x^2 + 2ax + a^2, so that x^2 + 2ax = (x + a) ^2 - a^2

We want to solve

x^2 + 3x = 7/4

By setting a = 3/2, we obtain

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

Therefore the given equation may be written as

(x + 3/2) ^2 - (3/2) ^2 = 7/4

(x + 3/2) ^2 - 9/4 = 7/4

(x + 3/2) ^2 = 7/4 + 9/4 = 16/4

(x + 3/2) ^2 = 4

Take square root of each side.

x + 3/2 = + / - 2

Therefore

x = + 2 - 3/2 = 1/2

or

x = - 2 - 3/2 = - 7/2

Answer: x = 1/2, or x = - 7/2