Solve by Factoring 5x^2+7x-34=0

$5 x^{2} + 7 x - 34 = 0$

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 $a \cdot c = 5 \cdot - 34 = - 170$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$5 x^{2} + 7 (x) - 34 = 0$

Rewrite $7$ as $- 10$ plus $17$

$5 x^{2} + (- 10 + 17) x - 34 = 0$

Apply the distributive property.

$5 x^{2} - 10 x + 17 x - 34 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 10 x) + 17 x - 34 = 0$

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

$5 x (x - 2) + 17 (x - 2) = 0$

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

$(x - 2) (5 x + 17) = 0$

Step 2

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

$x - 2 = 0$

$5 x + 17 = 0$

Step 3

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 4

Set $5 x + 17$ equal to $0$ and solve for $x$ .

Set $5 x + 17$ equal to $0$ .

$5 x + 17 = 0$

Solve $5 x + 17 = 0$ for $x$ .

Subtract $17$ from both sides of the equation.

$5 x = - 17$

Divide each term in $5 x = - 17$ by $5$ and simplify.

Divide each term in $5 x = - 17$ by $5$ .

$\frac{5 x}{5} = \frac{- 17}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 17}{5}$

Divide $x$ by $1$ .

$x = \frac{- 17}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{17}{5}$

Step 5

The final solution is all the values that make $(x - 2) (5 x + 17) = 0$ true.

$x = 2, - \frac{17}{5}$

Solve by Factoring 5x^2+7x-34=0

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