Question

find the solution set.
$8x^2 - 9x = -1$
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rearrange to standard quadratic form

$8x^2 - 9x + 1 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=8, b=-9, c=1$.
$$x=\frac{9\pm\sqrt{(-9)^2-4(8)(1)}}{2(8)}$$

Step3: Calculate discriminant

$\sqrt{81-32}=\sqrt{49}=7$

Step4: Solve for x values

$x_1=\frac{9+7}{16}=\frac{16}{16}=1$, $x_2=\frac{9-7}{16}=\frac{2}{16}=\frac{1}{8}$

Answer:

$1, \frac{1}{8}$