Solve the quadratic equation. Show all of your steps.
x^2 + 3x − 5 = 0
To solve the quadratic equation x^2 + 3x - 5 = 0, we can use the quadratic formula which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Given the equation x^2 + 3x - 5 = 0, we can identify a = 1, b = 3, and c = -5. Substituting these values into the quadratic formula, we have:
x = (-(3) ± sqrt((3)^2 - 4(1)(-5))) / 2(1)
x = (-3 ± sqrt(9 + 20)) / 2
x = (-3 ± sqrt(29)) / 2
Therefore, the solutions to the quadratic equation x^2 + 3x - 5 = 0 are:
x = (-3 + sqrt(29)) / 2
x = (-3 - sqrt(29)) / 2