Question

solve for the roots in simplest form using the quadratic formula:
$4x^2 - 4x = 3$
answer attempt 1 out of 2
additional solution no solution
$x = $
submit answer

Explanation:

Step1: Rewrite to standard quadratic form

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

Step2: Identify a, b, c values

$a=4,\ b=-4,\ c=-3$

Step3: Apply quadratic formula

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

Step4: Substitute values into formula

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

Step5: Simplify discriminant

$\sqrt{16 + 48} = \sqrt{64} = 8$

Step6: Simplify the expression

$x = \frac{4 \pm 8}{8}$

Step7: Calculate two roots

$x_1 = \frac{4+8}{8} = \frac{12}{8} = \frac{3}{2}$, $x_2 = \frac{4-8}{8} = \frac{-4}{8} = -\frac{1}{2}$

Answer:

$x = \frac{3}{2}$ and $x = -\frac{1}{2}$