Solve by Factoring 2x^2-x-28=0

$2 x^{2} - x - 28 = 0$

Step 1

Factor by grouping.

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 $a \cdot c = 2 \cdot - 28 = - 56$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$2 x^{2} - (x) - 28 = 0$

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

$2 x^{2} + (7 - 8) x - 28 = 0$

Apply the distributive property.

$2 x^{2} + 7 x - 8 x - 28 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 7 x) - 8 x - 28 = 0$

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

$x (2 x + 7) - 4 (2 x + 7) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 7$ .

$(2 x + 7) (x - 4) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x + 7 = 0$

$x - 4 = 0$

Step 3

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 4

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 5

The final solution is all the values that make $(2 x + 7) (x - 4) = 0$ true.

$x = - \frac{7}{2}, 4$

Solve by Factoring 2x^2-x-28=0

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