Question

What is the solution set for the equation 4x^2-8x+3=0?

Answer 1

\[4x^{2}-8x+3=0\]
Method 1: Factor a trinomial
(1 - 2x)(3 - 2x) = 0

When (1 - 2x) = 0
1 - 2x = 0
x = 0.5

When (3 - 2x) = 0
2x = 3
x = 1.5

Solution
x = {0.5, 1.5}

Method 2: Using Quadratic Formula:
\[x = \frac{ -b \pm \sqrt{b^{2} - 4ac} }{ 2a }\]
where a = 4, b = -8, c = 3,
\[x = \frac{ 8 \pm \sqrt{8^{2} - 4.4.3} }{ 2.4 }\]
x = {0.5, 1.5}