Algebra Examples

$2 x^{2} - 5 x = - 2$

Step 1

Add $2$ to both sides of the equation.

$2 x^{2} - 5 x + 2 = 0$

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 2 = 4$ and whose sum is $b = - 5$ .

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Step 2.1.1

Factor $- 5$ out of $- 5 x$ .

$2 x^{2} - 5 (x) + 2 = 0$

Step 2.1.2

Rewrite $- 5$ as $- 1$ plus $- 4$

$2 x^{2} + (- 1 - 4) x + 2 = 0$

Step 2.1.3

Apply the distributive property.

$2 x^{2} - 1 x - 4 x + 2 = 0$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) - 4 x + 2 = 0$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 1) - 2 (2 x - 1) = 0$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (x - 2) = 0$