Solve for x (x+4)(x-5)+3=0

$(x + 4) (x - 5) + 3 = 0$

Step 1

Simplify $(x + 4) (x - 5) + 3$ .

Simplify each term.

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

Apply the distributive property.

$x (x - 5) + 4 (x - 5) + 3 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 4 (x - 5) + 3 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 4 x + 4 \cdot - 5 + 3 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 + 4 x + 4 \cdot - 5 + 3 = 0$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x + 4 x + 4 \cdot - 5 + 3 = 0$

Multiply $4$ by $- 5$ .

$x^{2} - 5 x + 4 x - 20 + 3 = 0$

Add $- 5 x$ and $4 x$ .

$x^{2} - x - 20 + 3 = 0$

Add $- 20$ and $3$ .

$x^{2} - x - 17 = 0$

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 $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 17$ .

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot - 17}}{2 \cdot 1}$

Multiply $- 4$ by $- 17$ .

$x = \frac{1 \pm \sqrt{1 + 68}}{2 \cdot 1}$

Add $1$ and $68$ .

$x = \frac{1 \pm \sqrt{69}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{69}}{2}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1 + \sqrt{69}}{2}, \frac{1 - \sqrt{69}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 + \sqrt{69}}{2}, \frac{1 - \sqrt{69}}{2}$

Decimal Form:

$x = 4.65331193 \dots, - 3.65331193 \dots$

Solve for x (x+4)(x-5)+3=0

Related Questions

Support LCMGCF.com by disabling your adblocker.