Question

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

Answer 1

ANSWER

$x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2}$

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

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

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

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

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

$x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2}$

Answer 2

Answer:

$x_1=4.158$

$x_2=0.8416$

Step-by-step explanation:

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

The quadratic formula is

$\frac{-b\±\sqrt{b^2 -4ac}}{2a}$

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:

$x=\frac{-(-10)\±\sqrt{(-10)^2 -4(2(7)}}{2(2)}$

$x=\frac{5\±\sqrt{11}}{2}$

$x_1=4.158$

$x_2=0.8416$