Answer
The solution set is ${x = \frac{3 + 1\sqrt11}{2}, x = \frac{3 - 1\sqrt11}{2}}$
Work Step by Step
$2x^2-6x=1$
Step-1 : Write the equation in standard form by subtracting 1 from both sides.
$2x^2-6x-1=0$
Now, a = 2; b = -6; c = -1
The quadratic formula is:
$x = \frac{-b ± \sqrt{b^2-4ac}}{2a}$
Step 2: Substitute in the quadratic formula and solve:
$x = \frac{-(-6) ± \sqrt{(-6) ^2-(4 \times 2 \times -1)}}{2 \times 2}$
$x = \frac{6 ± \sqrt{36-(-8)}}{4}$
$x = \frac{6 ± \sqrt{36+8}}{4}$
$x = \frac{6 ± \sqrt44}{4}$
$x = \frac{6 ± \sqrt{11\times 4}}{4}$
$x = \frac{6 ± 2\sqrt{11}}{4}$
$x = \frac{2(3 ± 1\sqrt11)}{2 \times 2}$
$x = \frac{3 ± 1\sqrt11}{2}$
The solution set is ${x = \frac{3 + 1\sqrt11}{2}, x = \frac{3 - 1\sqrt11}{2}}$
