Solve Using the Quadratic Formula (7x+2)(5x-4)=0

$(7 x + 2) (5 x - 4) = 0$

Step 1

Simplify the left side.

Simplify $(7 x + 2) (5 x - 4)$ .

Expand $(7 x + 2) (5 x - 4)$ using the FOIL Method.

Apply the distributive property.

$7 x (5 x - 4) + 2 (5 x - 4) = 0$

Apply the distributive property.

$7 x (5 x) + 7 x \cdot - 4 + 2 (5 x - 4) = 0$

Apply the distributive property.

$7 x (5 x) + 7 x \cdot - 4 + 2 (5 x) + 2 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 5 x \cdot x + 7 x \cdot - 4 + 2 (5 x) + 2 \cdot - 4 = 0$

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

Move $x$ .

$7 \cdot 5 (x \cdot x) + 7 x \cdot - 4 + 2 (5 x) + 2 \cdot - 4 = 0$

Multiply $x$ by $x$ .

$7 \cdot 5 x^{2} + 7 x \cdot - 4 + 2 (5 x) + 2 \cdot - 4 = 0$

Multiply $7$ by $5$ .

$35 x^{2} + 7 x \cdot - 4 + 2 (5 x) + 2 \cdot - 4 = 0$

Multiply $- 4$ by $7$ .

$35 x^{2} - 28 x + 2 (5 x) + 2 \cdot - 4 = 0$

Multiply $5$ by $2$ .

$35 x^{2} - 28 x + 10 x + 2 \cdot - 4 = 0$

Multiply $2$ by $- 4$ .

$35 x^{2} - 28 x + 10 x - 8 = 0$

Add $- 28 x$ and $10 x$ .

$35 x^{2} - 18 x - 8 = 0$

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 $a = 35$ , $b = - 18$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{18 \pm \sqrt{{(- 18)}^{2} - 4 \cdot (35 \cdot - 8)}}{2 \cdot 35}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 18$ to the power of $2$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 35 \cdot - 8}}{2 \cdot 35}$

Multiply $- 4 \cdot 35 \cdot - 8$ .

Multiply $- 4$ by $35$ .

$x = \frac{18 \pm \sqrt{324 - 140 \cdot - 8}}{2 \cdot 35}$

Multiply $- 140$ by $- 8$ .

$x = \frac{18 \pm \sqrt{324 + 1120}}{2 \cdot 35}$

Add $324$ and $1120$ .

$x = \frac{18 \pm \sqrt{1444}}{2 \cdot 35}$

Rewrite $1444$ as $38^{2}$ .

$x = \frac{18 \pm \sqrt{38^{2}}}{2 \cdot 35}$

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

$x = \frac{18 \pm 38}{2 \cdot 35}$

Multiply $2$ by $35$ .

$x = \frac{18 \pm 38}{70}$

Simplify $\frac{18 \pm 38}{70}$ .

$x = \frac{9 \pm 19}{35}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{4}{5}, - \frac{2}{7}$

Solve Using the Quadratic Formula (7x+2)(5x-4)=0

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