Question

solve for x. write both solutions, separated by a comma. 5x² - 7x + 2 = 0 enter the correct answer.

Explanation:

Step1: Factor the quadratic equation

We need two numbers that multiply to $5\times2=10$ and add to $-7$. These numbers are $-5$ and $-2$. Rewrite and factor:
$$5x^2 -5x -2x +2 = 0$$
$$5x(x-1) -2(x-1) = 0$$
$$(5x-2)(x-1)=0$$

Step2: Set each factor to zero

Solve for $x$ in each factor:

Substep2a: Solve $5x-2=0$

$$5x=2 \implies x=\frac{2}{5}$$

Substep2b: Solve $x-1=0$

$$x=1$$

Answer:

$1, \frac{2}{5}$