Find the Roots (Zeros) (x+2)(x+5)-3x=0

$(x + 2) (x + 5) - 3 x = 0$

Simplify $(x + 2) (x + 5) - 3 x$ .

Simplify each term.

Expand $(x + 2) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) + 2 (x + 5) - 3 x = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 2 (x + 5) - 3 x = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 2 x + 2 \cdot 5 - 3 x = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 + 2 x + 2 \cdot 5 - 3 x = 0$

Move $5$ to the left of $x$ .

$x^{2} + 5 \cdot x + 2 x + 2 \cdot 5 - 3 x = 0$

Multiply $2$ by $5$ .

$x^{2} + 5 x + 2 x + 10 - 3 x = 0$

Add $5 x$ and $2 x$ .

$x^{2} + 7 x + 10 - 3 x = 0$

Subtract $3 x$ from $7 x$ .

$x^{2} + 4 x + 10 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = 4$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot 10)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$x = \frac{- 4 \pm \sqrt{16 - 40}}{2 \cdot 1}$

Subtract $40$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 24}}{2 \cdot 1}$

Rewrite $- 24$ as $- 1 (24)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 24}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{24}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 4 \pm i \cdot \sqrt{24}}{2 \cdot 1}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (6)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 6}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{6})}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{- 4 \pm 2 i \sqrt{6}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 i \sqrt{6}}{2}$

Simplify $\frac{- 4 \pm 2 i \sqrt{6}}{2}$ .

$x = - 2 \pm i \sqrt{6}$

Find the Roots (Zeros) (x+2)(x+5)-3x=0

Related Questions

Support LCMGCF.com by disabling your adblocker.