Question

Which of the following are solutions to the equation below?4x^2-12x+9=5

Answer 1

Answer:

$x=\frac{-\sqrt{5}+3}{2}$ and $x=\frac{\sqrt{5}+3}{2}$

Step-by-step explanation:

$4x^2-12x+9=5$

To solve for x we need to make right hand side 0

Subtract 5 on both sides

$4x^2-12x+4=0$

Divide whole equation by 4

$x^2-3x+1=0$

Apply quadratic formula to solve for x

$x=\frac{-b+-\sqrt{b^2-4ac}}{2a}$

the value of a=1, b=-3 and c=1

$x=\frac{-(-3)+-\sqrt{(-3)^2-4(1)(1)}}{2(1)}$

$x=\frac{3+-\sqrt{5}}{2}$

$x=\frac{-\sqrt{5}+3}{2}$ and $x=\frac{\sqrt{5}+3}{2}$

Answer 2

$4x^2-12x+9=5\\4x^2-12x+9-5=0\\4x^2-12x+4=0 \ \ \ |:4\\x^2-3x+1=0 \\ \\ x= \cfrac{3б \sqrt{(-3)^2-4} }{2}= \cfrac{3б \sqrt{9-4} }{2}= \cfrac{3б \sqrt{5} }{2}$

Correct answers are C and E