Question

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

Answer 1

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

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

Explanation:

x² + 3x - 5 = 0

Using quadratic formula:

x = [-3 +/- sqrt(3² - 4(1)(-5)]/2

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

Answer 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