Question

Find the solutions to the equation 4x2 - 8x + 3 = 0

Answer 1

Steps

So to find the solutions, I will be factoring by grouping. Firstly, what two terms have a product of 12x² and a sum of -8x? That would be -2x and -6x. Replace -8x with -2x - 6x:

$4x^2-2x-6x+3=0$

Next, factor 4x² - 2x and -6x + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:

$2x(2x-1)-3(2x-1)=0$

Now you can rewrite it as:

$(2x-3)(2x-1)=0$

Now, apply the zero product property and solve:

$2x-3=0\\2x=3\\x=\frac{3}{2}\ \textsf{OR}\ 1.5\\\\2x-1=0\\2x=1\\x=\frac{1}{2}\ \textsf{OR}\ 0.5$

Answer

In short, x = 3/2 (1.5) and 1/2 (0.5).