Algebra Examples

x^{2} - 18 x + 81 = 0

$x^{2} - 18 x + 81 = 0$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^{2} - 4 (a c)

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of

a

$a$ ,

b

$b$ , and

c

$c$ .

{(- 18)}^{2} - 4 (1 \cdot 81)

${(- 18)}^{2} - 4 (1 \cdot 81)$

Step 3

Evaluate the result to find the discriminant.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise

- 18

$- 18$ to the power of

2

$2$ .

324 - 4 (1 \cdot 81)

$324 - 4 (1 \cdot 81)$

Step 3.1.2

Multiply

- 4 (1 \cdot 81)

$- 4 (1 \cdot 81)$ .

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Step 3.1.2.1

Multiply

81

$81$ by

1

$1$ .

324 - 4 \cdot 81

$324 - 4 \cdot 81$

Step 3.1.2.2

Multiply

- 4

$- 4$ by

81

$81$ .

324 - 324

$324 - 324$

324 - 324

$324 - 324$

324 - 324

$324 - 324$

Step 3.2

Subtract

324

$324$ from

324

$324$ .

0

$0$

0

$0$