Question

Use the quadratic formula to solve the equation​ 4x2−10x+5=0.

Answer 1

We have to use the quadratic formula:

$x= \frac{-b±\sqrt{b^{2}-4ac}}{2a}$

in your equation:
a = 4
b = -10
c = 5

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

we will do the positive part first:
$x= \frac{10+ \sqrt{(-10)^{2}-4(4)(5)} }{2(4)} \\ x= \frac{10+ \sqrt{100-4(20)} }{8} \\ x= \frac{10+ \sqrt{100-80} }{8} \\ x= \frac{10+ \sqrt{20} }{8}$

$x= \frac{10+2 \sqrt{5} }{8} \\ x= \frac{2(5+\sqrt{5})}{8}$

cancel common terms:
$x = \frac{2(5+\sqrt{5})}{2(4)} \\ x= \frac{5+\sqrt{5}}{4}$

Now for the negative root:
$x= \frac{10- \sqrt{(-10)^{2}-4(4)(5)} }{2(4)} \\ x= \frac{10- \sqrt{100-4(20)} }{8} \\ x= \frac{10- \sqrt{100-80} }{8} \\ x= \frac{10- \sqrt{20} }{8}$

$x= \frac{10-2 \sqrt{5} }{8} \\ x= \frac{2(5-\sqrt{5})}{8} \\ x= \frac{5-\sqrt{5}}{4}$

Answer 2

A=4 b=-10 c=5
10+-√100-(4)(4)(5)/8
10+-√20/8
10+-2√5/8
x= (5+√5)/4 and x =(5-√5)/4
the parentheses just mean that it is all over 4