Solve Using the Quadratic Formula (5x+4)(x+1)=2

$(5 x + 4) (x + 1) = 2$

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $(5 x + 4) (x + 1)$ .

Expand $(5 x + 4) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$5 x (x + 1) + 4 (x + 1) = 2$

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 1 + 4 (x + 1) = 2$

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 1 + 4 x + 4 \cdot 1 = 2$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$5 (x \cdot x) + 5 x \cdot 1 + 4 x + 4 \cdot 1 = 2$

Multiply $x$ by $x$ .

$5 x^{2} + 5 x \cdot 1 + 4 x + 4 \cdot 1 = 2$

Multiply $5$ by $1$ .

$5 x^{2} + 5 x + 4 x + 4 \cdot 1 = 2$

Multiply $4$ by $1$ .

$5 x^{2} + 5 x + 4 x + 4 = 2$

Add $5 x$ and $4 x$ .

$5 x^{2} + 9 x + 4 = 2$

Subtract $2$ from both sides of the equation.

$5 x^{2} + 9 x + 4 - 2 = 0$

Subtract $2$ from $4$ .

$5 x^{2} + 9 x + 2 = 0$

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 $a = 5$ , $b = 9$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (5 \cdot 2)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 5 \cdot 2}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 2$ .

Multiply $- 4$ by $5$ .

$x = \frac{- 9 \pm \sqrt{81 - 20 \cdot 2}}{2 \cdot 5}$

Multiply $- 20$ by $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 40}}{2 \cdot 5}$

Subtract $40$ from $81$ .

$x = \frac{- 9 \pm \sqrt{41}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 9 \pm \sqrt{41}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{41}}{10}$

Decimal Form:

$x = - 0.25968757 \dots, - 1.54031242 \dots$

Solve Using the Quadratic Formula (5x+4)(x+1)=2

Related Questions

Support LCMGCF.com by disabling your adblocker.