Question

Solve this quadratic equation using the quadratic formula. 2x 2 - 10x + 7 = 0

Answer 1

`x_1=4.158`

`x_2=0.8416`

Explanation:

For an equation of the form
`ax^2 +bx +c`

The quadratic formula is

`(-b\±√(b^2 -4ac))/(2a)`

In this case the equation is:

`2x^2 - 10x + 7 = 0`

Then

`a= 2\\b= -10\\c= 7`

Therefore, using the quadratic formula we have:

`x=(-(-10)\±√((-10)^2 -4(2(7)))/(2(2))`

`x=(5\±√(11))/(2)`

`x_1=4.158`

`x_2=0.8416`

Answer 2

`x = ( 5 )/(2) - \frac{\sqrt {11} } {2} \: or \: x = ( 5 )/(2) + \frac{\sqrt {11} } {2}`

EXPLANATION

The given quadratic equation is:

`2{x}^(2) - 10x + 7 = 0`

Comparing this equation to

`a{x}^(2) + bx + c = 0`

we have

a=2, b=-10 and c=7.

The solution is given by the quadratic formula;

`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a}`

We plug in the values to get,

`x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^(2) - 4(2)(7) } }{2(2)}`

This implies that

`x = \frac{ 10 \pm \sqrt{ {100} - 56 } }{4}`

`x = \frac{ 10 \pm \sqrt {44 } }{4}`

`x = \frac{ 10 \pm 2\sqrt {11 } }{4}`

`x = \frac{ 5 \pm \sqrt {11 } }{2}`

`x = ( 5 )/(2) - \frac{\sqrt {11} } {2} \: or \: x = ( 5 )/(2) + \frac{\sqrt {11} } {2}`