Question

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

Answer 1

x= 0.53 and x = -0.63

Explanation:

Quadratic formula:- ax² + bx + c

x = [-b ± √(b² - 4ac)]/2

It is given that, quadratic equation 11x2 – 4x = 1

To find the value of x

11x2 – 4x = 1

⇒11x2 – 4x - 1 = 0

a = 11

b = -4

c = -1

x = [-b ± √(b² - 4ac)]/2

x = [-(-4) ± √((-4)² - 4*11*-1)]/2*11

x = [4±√(16 +44)]/22

x = [4±√(60)]/22

x = [4±7.7]/22

x= 0.53 and x = -0.63

Answer 2

Hello!

The answer is:

`x1=0.53\\x2=-0.17`

Why?

The quadratic formula is:

`x=\frac{-b+-\sqrt{b^(2)-4*a*c } }{2*a}`

We have that:

`a=11\\b=-4\\c=-1`

By substituting we have:

`x=\frac{4+-\sqrt{-4^(2)-4*11*-1 } }{2*11}=(4+-√(16+44) )/(22)=(4+-√(60) )/(22)=(4+-(7.75))/(22)`

`x1=(4+7.75)/(22)=0.53\\\\x2=(4-7.75)/(22) =-0.17`

Have a nice day!