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:

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

Cancel the common terms:

$x=\frac{5±\sqrt{5} }{4}$