Solve Using the Quadratic Formula (2x-5)(3x-1)=0

$(2 x - 5) (3 x - 1) = 0$

Step 1

Simplify the left side.

Simplify $(2 x - 5) (3 x - 1)$ .

Expand $(2 x - 5) (3 x - 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x - 1) - 5 (3 x - 1) = 0$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 1 - 5 (3 x - 1) = 0$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 1 - 5 (3 x) - 5 \cdot - 1 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot - 1 - 5 (3 x) - 5 \cdot - 1 = 0$

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

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot - 1 - 5 (3 x) - 5 \cdot - 1 = 0$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot - 1 - 5 (3 x) - 5 \cdot - 1 = 0$

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot - 1 - 5 (3 x) - 5 \cdot - 1 = 0$

Multiply $- 1$ by $2$ .

$6 x^{2} - 2 x - 5 (3 x) - 5 \cdot - 1 = 0$

Multiply $3$ by $- 5$ .

$6 x^{2} - 2 x - 15 x - 5 \cdot - 1 = 0$

Multiply $- 5$ by $- 1$ .

$6 x^{2} - 2 x - 15 x + 5 = 0$

Subtract $15 x$ from $- 2 x$ .

$6 x^{2} - 17 x + 5 = 0$

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 $a = 6$ , $b = - 17$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{17 \pm \sqrt{{(- 17)}^{2} - 4 \cdot (6 \cdot 5)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 17$ to the power of $2$ .

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 6 \cdot 5}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot 5$ .

Multiply $- 4$ by $6$ .

$x = \frac{17 \pm \sqrt{289 - 24 \cdot 5}}{2 \cdot 6}$

Multiply $- 24$ by $5$ .

$x = \frac{17 \pm \sqrt{289 - 120}}{2 \cdot 6}$

Subtract $120$ from $289$ .

$x = \frac{17 \pm \sqrt{169}}{2 \cdot 6}$

Rewrite $169$ as $13^{2}$ .

$x = \frac{17 \pm \sqrt{13^{2}}}{2 \cdot 6}$

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

$x = \frac{17 \pm 13}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{17 \pm 13}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{2}, \frac{1}{3}$

Solve Using the Quadratic Formula (2x-5)(3x-1)=0

Related Questions

Support LCMGCF.com by disabling your adblocker.