Question

Use the quadratic formula to solve the equation​.

4x^2−10x+5=0

Answer 1

Quadratic formula:

`x=\frac{-b±\sqrt{b^(2)-4ac } }{2a}`

What do we have:

a=4

b=-10

c=5

Substitude:

`x=\frac{10±\sqrt{b^(2)-4(4)(5)}}{2(a)}`

Solve:

`x=\frac{10±\sqrt{(-10)^(2)-4(4)(5)}}{2(4)}\\\\x=(10±√(100-4(20)))/(8)\\\\x=(10±√(100-4(20)))/(8)\\\\x=(10±√(100-80))/(8)\\\\x=(10±√(20))/(8)\\\\x=(10±2√(5 ))/(8)\\\\x=(2(±5√(5) ))/(2(4))`

Cancel the common terms:

`x=(5±√(5) )/(4)`