Algebra Examples

$n^{2} = 9 n - 20$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $9 n$ from both sides of the equation.

$n^{2} - 9 n = - 20$

Step 1.2

Add $20$ to both sides of the equation.

$n^{2} - 9 n + 20 = 0$

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 $a = 1$ , $b = - 9$ , and $c = 20$ into the quadratic formula and solve for $n$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot 20)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$n = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot 20}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 20$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$n = \frac{9 \pm \sqrt{81 - 4 \cdot 20}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $20$ .

$n = \frac{9 \pm \sqrt{81 - 80}}{2 \cdot 1}$

Step 4.1.3

Subtract $80$ from $81$ .

$n = \frac{9 \pm \sqrt{1}}{2 \cdot 1}$

Step 4.1.4

Any root of $1$ is $1$ .

$n = \frac{9 \pm 1}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$n = \frac{9 \pm 1}{2}$

Step 5

The final answer is the combination of both solutions.

$n = 5, 4$