Answer: x = +- radical 61 by 2 - 5/2
Step -by - step
x^2 + 5x - 9 = 0
Add 9 to both sides
x^2 + 5x = 9
To create a trinomial square on the left side of the equation, find the value that is equal to the square of half of b.
( b/2 )^2 = ( 5/2 )^2
Add term to each side of the equation.
x^2 + 5x + ( 5/2 )^2 = 9 + ( 5/2 )^2
x^2 + 5x + 25/4 = 9 + 25/4
Write 9 as a fractor with a common denominator, multiply by 4/4.
x^2 + 5x + 25/4 = 9 x 4/4 + 25/4
x^2 + 5x + 25/4 = 9 x 4 + 25 / 4
x^2 + 5x + 25/4 = 61/4
Factor the perfect trinomial square into
( x + 5/2 )^2 .
( x + 5/2 )^2 = 61/4
x + 5/2 = +- root 61 by 4