The equation x^2 + 6x - 5 = 0 is a quadratic equation, and you can solve it for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation:
a is the coefficient of the x^2 term, which is 1 in this case.
b is the coefficient of the x term, which is 6 in this case.
c is the constant term, which is -5 in this case.
Now, plug these values into the quadratic formula:
x = (-6 ± √(6² - 4(1)(-5))) / (2(1))
x = (-6 ± √(36 + 20)) / 2
x = (-6 ± √56) / 2
x = (-6 ± 2√14) / 2
Now, simplify by dividing both terms in the numerator by 2:
x = -3 ± √14
So, the solutions to the equation x^2 + 6x - 5 = 0 are:
x₁ = -3 + √14 x₂ = -3 - √14
