how do you solve this...?

x² + 3x - 1 = 0
x² + 3/2x = 1 + (3/2)²
x² + 3/2x = 4/4 + 9/4
(x + 3/2)² = 13/4
x + 1.5 = 1.8027757

x = 1.8027757 - 1.5, x = 0.3027757
x = - 1.8027757 - 1.5, x = - 3.3027757

Answer: x = 0.3027757, - 3.3027757

Proof that x = 0.3027757:
0.3027757² + 3(0.3027757) = 1
0.091673 + 0.908327 = 1
1 = 1

Proof that x = - 3.3027757:
- 3.3027757² + 3(- 3.3027757) = 1
10.9083271 - 9.9083271 = 1
1 = 1

x=(-3(plusorminus)sqrt(13))/2

x = [ - b ± √ (b ² - 4 a c ) ] / 2 a
x = [ - 3 ± √ (9 + 4) ] / 2
x = [ - 3 ± √ (13) ] / 2 is exact answer.

x^2 + 3x - 1 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = 3
c = -1

x = [-3 ±√(9 + 4)]/2
x = [-3 ±√13]/2

∴ x = [-3 ±√13]/2

To solve this, you'll need to use the quadratic formula:

with ax^2+bx+c=0,
x = (-b +/- sqrt(b^2-4ac))/2a

with x^2+3x-1=0
a=1, b=3, c= -1

x = (-b +/- sqrt(b^2-4ac))/2a
x = (-3 +/- sqrt(3^2-4*1*-1))/2*1
x = (-3 +/- sqrt(9-(-4))/2
x = (-3 +/- sqrt(13)/2
x = (-3 + sqrt(13)/2 and x = (-3 - sqrt(13)/2