Solve Using the Quadratic Formula (x+2)(x-3)=-2

$(x + 2) (x - 3) = - 2$

Step 1

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

Simplify the left side.

Simplify $(x + 2) (x - 3)$ .

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

Apply the distributive property.

$x (x - 3) + 2 (x - 3) = - 2$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 2 (x - 3) = - 2$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 2 x + 2 \cdot - 3 = - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 + 2 x + 2 \cdot - 3 = - 2$

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x + 2 x + 2 \cdot - 3 = - 2$

Multiply $2$ by $- 3$ .

$x^{2} - 3 x + 2 x - 6 = - 2$

Add $- 3 x$ and $2 x$ .

$x^{2} - x - 6 = - 2$

Add $2$ to both sides of the equation.

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

Add $- 6$ and $2$ .

$x^{2} - x - 4 = 0$

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 $a = 1$ , $b = - 1$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot - 4)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$x = \frac{1 \pm \sqrt{1 + 16}}{2 \cdot 1}$

Add $1$ and $16$ .

$x = \frac{1 \pm \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{17}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{17}}{2}$

Decimal Form:

$x = 2.56155281 \dots, - 1.56155281 \dots$

Solve Using the Quadratic Formula (x+2)(x-3)=-2

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