Solve Using the Quadratic Formula (2x-7)(4x+10)=0

$(2 x - 7) (4 x + 10) = 0$

Step 1

Simplify the left side.

Simplify $(2 x - 7) (4 x + 10)$ .

Expand $(2 x - 7) (4 x + 10)$ using the FOIL Method.

Apply the distributive property.

$2 x (4 x + 10) - 7 (4 x + 10) = 0$

Apply the distributive property.

$2 x (4 x) + 2 x \cdot 10 - 7 (4 x + 10) = 0$

Apply the distributive property.

$2 x (4 x) + 2 x \cdot 10 - 7 (4 x) - 7 \cdot 10 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x \cdot x + 2 x \cdot 10 - 7 (4 x) - 7 \cdot 10 = 0$

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

Move $x$ .

$2 \cdot 4 (x \cdot x) + 2 x \cdot 10 - 7 (4 x) - 7 \cdot 10 = 0$

Multiply $x$ by $x$ .

$2 \cdot 4 x^{2} + 2 x \cdot 10 - 7 (4 x) - 7 \cdot 10 = 0$

Multiply $2$ by $4$ .

$8 x^{2} + 2 x \cdot 10 - 7 (4 x) - 7 \cdot 10 = 0$

Multiply $10$ by $2$ .

$8 x^{2} + 20 x - 7 (4 x) - 7 \cdot 10 = 0$

Multiply $4$ by $- 7$ .

$8 x^{2} + 20 x - 28 x - 7 \cdot 10 = 0$

Multiply $- 7$ by $10$ .

$8 x^{2} + 20 x - 28 x - 70 = 0$

Subtract $28 x$ from $20 x$ .

$8 x^{2} - 8 x - 70 = 0$

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 $a = 8$ , $b = - 8$ , and $c = - 70$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (8 \cdot - 70)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 8 \cdot - 70}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 70$ .

Multiply $- 4$ by $8$ .

$x = \frac{8 \pm \sqrt{64 - 32 \cdot - 70}}{2 \cdot 8}$

Multiply $- 32$ by $- 70$ .

$x = \frac{8 \pm \sqrt{64 + 2240}}{2 \cdot 8}$

Add $64$ and $2240$ .

$x = \frac{8 \pm \sqrt{2304}}{2 \cdot 8}$

Rewrite $2304$ as $48^{2}$ .

$x = \frac{8 \pm \sqrt{48^{2}}}{2 \cdot 8}$

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

$x = \frac{8 \pm 48}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{8 \pm 48}{16}$

Simplify $\frac{8 \pm 48}{16}$ .

$x = \frac{1 \pm 6}{2}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{7}{2}, - \frac{5}{2}$

Solve Using the Quadratic Formula (2x-7)(4x+10)=0

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