Algebra Examples

${6 i, 6 i}$

$x = 6 i$ is a double root for the quadratic equation, which means that $x - 6 i$ and $x - 6 i$ are the factors of the quadratic equation.

$(x - 6 i) (x - 6 i) = 0$

Expand $(x - 6 i) (x - 6 i)$ using the FOIL Method.

Tap for more steps...

Apply the distributive property.

$x (x - 6 i) - 6 i (x - 6 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 6 i) - 6 i (x - 6 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 6 i) - 6 i x - 6 i (- 6 i) = 0$

Simplify and combine like terms.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $x$ by $x$ .

$x^{2} + x (- 6 i) - 6 i x - 6 i (- 6 i) = 0$

Multiply $- 6 i (- 6 i)$ .

Tap for more steps...

Multiply $- 6$ by $- 6$ .

$x^{2} + x (- 6 i) - 6 i x + 36 i i = 0$

Raise $i$ to the power of $1$ .

$x^{2} + x (- 6 i) - 6 i x + 36 (i i) = 0$

Raise $i$ to the power of $1$ .

$x^{2} + x (- 6 i) - 6 i x + 36 (i i) = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} + x (- 6 i) - 6 i x + 36 i^{1 + 1} = 0$

Add $1$ and $1$ .

$x^{2} + x (- 6 i) - 6 i x + 36 i^{2} = 0$

Rewrite $i^{2}$ as $- 1$ .

$x^{2} + x (- 6 i) - 6 i x + 36 \cdot - 1 = 0$

Multiply $36$ by $- 1$ .

$x^{2} + x (- 6 i) - 6 i x - 36 = 0$

Move $i$ .

$x^{2} - 6 \cdot (x i) - 6 x i - 36 = 0$

Subtract $6 x i$ from $- 6 \cdot x i$ .

$x^{2} - 12 x i - 36 = 0$

The standard quadratic equation using the given set of solutions ${6 i, 6 i}$ is $y = x^{2} - 12 x i - 36$ .

$y = x^{2} - 12 x i - 36$