Solve by Factoring 2x^2=17x+55

$2 x^{2} = 17 x + 55$

Step 1

Move all the expressions to the left side of the equation.

Subtract $17 x$ from both sides of the equation.

$2 x^{2} - 17 x = 55$

Subtract $55$ from both sides of the equation.

$2 x^{2} - 17 x - 55 = 0$

Step 2

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 $a \cdot c = 2 \cdot - 55 = - 110$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$2 x^{2} - 17 x - 55 = 0$

Rewrite $- 17$ as $5$ plus $- 22$

$2 x^{2} + (5 - 22) x - 55 = 0$

Apply the distributive property.

$2 x^{2} + 5 x - 22 x - 55 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 5 x) - 22 x - 55 = 0$

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

$x (2 x + 5) - 11 (2 x + 5) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

$(2 x + 5) (x - 11) = 0$

Step 3

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

$2 x + 5 = 0$

$x - 11 = 0$

Step 4

Set $2 x + 5$ equal to $0$ and solve for $x$ .

Set $2 x + 5$ equal to $0$ .

$2 x + 5 = 0$

Solve $2 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$2 x = - 5$

Divide each term in $2 x = - 5$ by $2$ and simplify.

Divide each term in $2 x = - 5$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

Set $x - 11$ equal to $0$ and solve for $x$ .

Set $x - 11$ equal to $0$ .

$x - 11 = 0$

Add $11$ to both sides of the equation.

$x = 11$

Step 6

The final solution is all the values that make $(2 x + 5) (x - 11) = 0$ true.

$x = - \frac{5}{2}, 11$

Solve by Factoring 2x^2=17x+55

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