Finite Math Examples

$4 x \cdot x - 2 = 7 x$

Step 1

Subtract $7 x$ from both sides of the equation.

$4 x \cdot x - 2 - 7 x = 0$

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

$4 (x \cdot x) - 2 - 7 x = 0$

Step 2.2

Multiply $x$ by $x$ .

$4 x^{2} - 2 - 7 x = 0$

Step 3

Factor by grouping.

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Step 3.1

Reorder terms.

$4 x^{2} - 7 x - 2 = 0$

Step 3.2

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 $a \cdot c = 4 \cdot - 2 = - 8$ and whose sum is $b = - 7$ .

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Step 3.2.1

Factor $- 7$ out of $- 7 x$ .

$4 x^{2} - 7 x - 2 = 0$

Step 3.2.2

Rewrite $- 7$ as $1$ plus $- 8$

$4 x^{2} + (1 - 8) x - 2 = 0$

Step 3.2.3

Apply the distributive property.

$4 x^{2} + 1 x - 8 x - 2 = 0$

Step 3.2.4

Multiply $x$ by $1$ .

$4 x^{2} + x - 8 x - 2 = 0$

Step 3.3

Factor out the greatest common factor from each group.

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Step 3.3.1

Group the first two terms and the last two terms.

$(4 x^{2} + x) - 8 x - 2 = 0$

Step 3.3.2

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

$x (4 x + 1) - 2 (4 x + 1) = 0$

Step 3.4

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (x - 2) = 0$