Solve Using the Quadratic Formula x^2+nx+25

$x^{2} + n x + 25$

Step 1

Set $x^{2} + n x + 25$ equal to $0$ .

$x^{2} + n x + 25 = 0$

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 $a = 1$ , $b = n$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{- n \pm \sqrt{n^{2} - 4 \cdot (1 \cdot 25)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Rewrite $4 \cdot 1 \cdot 25$ as ${(2 \cdot 1 \cdot 5)}^{2}$ .

$x = \frac{- n \pm \sqrt{n^{2} - {(2 \cdot 1 \cdot 5)}^{2}}}{2 \cdot 1}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = n$ and $b = 2 \cdot 1 \cdot 5$ .

$x = \frac{- n \pm \sqrt{(n + 2 \cdot 1 \cdot 5) (n - (2 \cdot 1 \cdot 5))}}{2 \cdot 1}$

Simplify.

Multiply $2 \cdot 1 \cdot 5$ .

Multiply $2$ by $1$ .

$x = \frac{- n \pm \sqrt{(n + 2 \cdot 5) (n - (2 \cdot 1 \cdot 5))}}{2 \cdot 1}$

Multiply $2$ by $5$ .

$x = \frac{- n \pm \sqrt{(n + 10) (n - (2 \cdot 1 \cdot 5))}}{2 \cdot 1}$

Multiply $- (2 \cdot 1 \cdot 5)$ .

Multiply $2$ by $1$ .

$x = \frac{- n \pm \sqrt{(n + 10) (n - (2 \cdot 5))}}{2 \cdot 1}$

Multiply $2$ by $5$ .

$x = \frac{- n \pm \sqrt{(n + 10) (n - 1 \cdot 10)}}{2 \cdot 1}$

Multiply $- 1$ by $10$ .

$x = \frac{- n \pm \sqrt{(n + 10) (n - 10)}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- n \pm \sqrt{(n + 10) (n - 10)}}{2}$

Solve Using the Quadratic Formula x^2+nx+25

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