Solve Using the Quadratic Formula (2x-1)(x+4)=0

$(2 x - 1) (x + 4) = 0$

Step 1

Simplify the left side.

Simplify $(2 x - 1) (x + 4)$ .

Expand $(2 x - 1) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$2 x (x + 4) - 1 (x + 4) = 0$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 4 - 1 (x + 4) = 0$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 4 - 1 x - 1 \cdot 4 = 0$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 4 - 1 x - 1 \cdot 4 = 0$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 4 - 1 x - 1 \cdot 4 = 0$

Multiply $4$ by $2$ .

$2 x^{2} + 8 x - 1 x - 1 \cdot 4 = 0$

Rewrite $- 1 x$ as $- x$ .

$2 x^{2} + 8 x - x - 1 \cdot 4 = 0$

Multiply $- 1$ by $4$ .

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

Subtract $x$ from $8 x$ .

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

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 $a = 2$ , $b = 7$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (2 \cdot - 4)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 2 \cdot - 4}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 8 \cdot - 4}}{2 \cdot 2}$

Multiply $- 8$ by $- 4$ .

$x = \frac{- 7 \pm \sqrt{49 + 32}}{2 \cdot 2}$

Add $49$ and $32$ .

$x = \frac{- 7 \pm \sqrt{81}}{2 \cdot 2}$

Rewrite $81$ as $9^{2}$ .

$x = \frac{- 7 \pm \sqrt{9^{2}}}{2 \cdot 2}$

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

$x = \frac{- 7 \pm 9}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 7 \pm 9}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1}{2}, - 4$

Solve Using the Quadratic Formula (2x-1)(x+4)=0

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