Solve Using the Quadratic Formula (x+4)(2x-9)=0

$(x + 4) (2 x - 9) = 0$

Step 1

Simplify the left side.

Simplify $(x + 4) (2 x - 9)$ .

Expand $(x + 4) (2 x - 9)$ using the FOIL Method.

Apply the distributive property.

$x (2 x - 9) + 4 (2 x - 9) = 0$

Apply the distributive property.

$x (2 x) + x \cdot - 9 + 4 (2 x - 9) = 0$

Apply the distributive property.

$x (2 x) + x \cdot - 9 + 4 (2 x) + 4 \cdot - 9 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 9 + 4 (2 x) + 4 \cdot - 9 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + x \cdot - 9 + 4 (2 x) + 4 \cdot - 9 = 0$

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot - 9 + 4 (2 x) + 4 \cdot - 9 = 0$

Move $- 9$ to the left of $x$ .

$2 x^{2} - 9 \cdot x + 4 (2 x) + 4 \cdot - 9 = 0$

Multiply $2$ by $4$ .

$2 x^{2} - 9 x + 8 x + 4 \cdot - 9 = 0$

Multiply $4$ by $- 9$ .

$2 x^{2} - 9 x + 8 x - 36 = 0$

Add $- 9 x$ and $8 x$ .

$2 x^{2} - x - 36 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 2$ , $b = - 1$ , and $c = - 36$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (2 \cdot - 36)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 2 \cdot - 36}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 36$ .

Multiply $- 4$ by $2$ .

$x = \frac{1 \pm \sqrt{1 - 8 \cdot - 36}}{2 \cdot 2}$

Multiply $- 8$ by $- 36$ .

$x = \frac{1 \pm \sqrt{1 + 288}}{2 \cdot 2}$

Add $1$ and $288$ .

$x = \frac{1 \pm \sqrt{289}}{2 \cdot 2}$

Rewrite $289$ as $17^{2}$ .

$x = \frac{1 \pm \sqrt{17^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{1 \pm 17}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{1 \pm 17}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{9}{2}, - 4$

Solve Using the Quadratic Formula (x+4)(2x-9)=0

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