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

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

Step 1

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

Simplify the left side.

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $1$ .

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

Multiply $- 5$ by $1$ .

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

Subtract $5 x$ from $2 x$ .

$2 x^{2} - 3 x - 5 = 2$

Subtract $2$ from both sides of the equation.

$2 x^{2} - 3 x - 5 - 2 = 0$

Subtract $2$ from $- 5$ .

$2 x^{2} - 3 x - 7 = 0$

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 $a = 2$ , $b = - 3$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (2 \cdot - 7)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 2 \cdot - 7}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 7$ .

Multiply $- 4$ by $2$ .

$x = \frac{3 \pm \sqrt{9 - 8 \cdot - 7}}{2 \cdot 2}$

Multiply $- 8$ by $- 7$ .

$x = \frac{3 \pm \sqrt{9 + 56}}{2 \cdot 2}$

Add $9$ and $56$ .

$x = \frac{3 \pm \sqrt{65}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{3 \pm \sqrt{65}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{65}}{4}$

Decimal Form:

$x = 2.76556443 \dots, - 1.26556443 \dots$

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

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