Solve by Factoring 14x^2+3x-2=0

$14 x^{2} + 3 x - 2 = 0$

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 $a \cdot c = 14 \cdot - 2 = - 28$ and whose sum is $b = 3$ .

Factor $3$ out of $3 x$ .

$14 x^{2} + 3 (x) - 2 = 0$

Rewrite $3$ as $- 4$ plus $7$

$14 x^{2} + (- 4 + 7) x - 2 = 0$

Apply the distributive property.

$14 x^{2} - 4 x + 7 x - 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 4 x) + 7 x - 2 = 0$

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

$2 x (7 x - 2) + 1 (7 x - 2) = 0$

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

$(7 x - 2) (2 x + 1) = 0$

Step 2

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

$7 x - 2 = 0$

$2 x + 1 = 0$

Step 3

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

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

$7 x - 2 = 0$

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

Add $2$ to both sides of the equation.

$7 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 5

The final solution is all the values that make $(7 x - 2) (2 x + 1) = 0$ true.

$x = \frac{2}{7}, - \frac{1}{2}$

Solve by Factoring 14x^2+3x-2=0

Related Questions

Support LCMGCF.com by disabling your adblocker.