Question

Solve the following quadratic equation using the quadratic formula.

Answer 1

`x=(8+√(-36) )/(10)`

`x=(8-√(-36) )/(10)`

Explanation:

5x² - 8x + 5 = 0

`x=\frac{-b±\sqrt{b^(2) -4ac} }{2a}`

Ignore the A before the ±, it wouldn't let me type it correctly.

a = 5

b = - 8

c = 5

`x=\frac{-(-8)±\sqrt{-8^(2) -4((5)(5))} }{2(5)}`

`x=(8±√(64 -4((5)(5))) )/(2(5))`

`x=(8±√(64 -100) )/(2(5))`

`x=(8±√(-36) )/(10)`

No solution because, you need the square root of a negative number. That isn't really possible.

`x=(8+√(-36) )/(10)`

`x=(8-√(-36) )/(10)`

Answer 2

The quadratic formula tells you the solution to
ax² +bx +c = 0
is

`x=\frac{-b \pm \sqrt{b^(2)-4ac}}{2a}`
Plugging in the values a=5, b=-8, c=5, you get

`x=\frac{8 \pm \sqrt{(-8)^(2)-4\cdot 5\cdot 5}}{2\cdot 5} = (8 \pm √(-36))/(10) = (4 \pm 3i)/(5)`

Your solution is

`x=(4-3i)/(5),x=(4+3i)/(5)`