Solve the quadratic equation. Show all of your steps. x^2+3x-5=0

x = [-3 + sqrt (29) ]/2

x = [-3 - sqrt (29) ]/2

Step-by-step explanation:

x² + 3x - 5 = 0

Using quadratic formula:

x = [-3 + / - sqrt (3² - 4 (1) (-5) ]/2

x = [-3 + / - sqrt (29) ]/2

x = sqrt (29) / 2 - 3/2 or x = - 3/2 - sqrt (29) / 2

Step-by-step explanation by completing the square:

Solve for x over the real numbers:

x^2 + 3 x - 5 = 0

Add 5 to both sides:

x^2 + 3 x = 5

Add 9/4 to both sides:

x^2 + 3 x + 9/4 = 29/4

Write the left hand side as a square:

(x + 3/2) ^2 = 29/4

Take the square root of both sides:

x + 3/2 = sqrt (29) / 2 or x + 3/2 = - sqrt (29) / 2

Subtract 3/2 from both sides:

x = sqrt (29) / 2 - 3/2 or x + 3/2 = - sqrt (29) / 2

Subtract 3/2 from both sides:

Answer: x = sqrt (29) / 2 - 3/2 or x = - 3/2 - sqrt (29) / 2