Find the Quadratic Equation 7i , -7i

$7 i$ , $- 7 i$

Step 1

$x = 7 i$ and $x = - 7 i$ are the two real distinct solutions for the quadratic equation, which means that $x - 7 i$ and $x - (- 7 i)$ are the factors of the quadratic equation.

$(x - 7 i) (x + 7 i) = 0$

Step 2

Expand $(x - 7 i) (x + 7 i)$ using the FOIL Method.

Apply the distributive property.

$x (x + 7 i) - 7 i (x + 7 i) = 0$

Apply the distributive property.

$x \cdot x + x (7 i) - 7 i (x + 7 i) = 0$

Apply the distributive property.

$x \cdot x + x (7 i) - 7 i x - 7 i (7 i) = 0$

Step 3

Simplify terms.

Combine the opposite terms in $x \cdot x + x (7 i) - 7 i x - 7 i (7 i)$ .

Reorder the factors in the terms $x (7 i)$ and $- 7 i x$ .

$x \cdot x + 7 i x - 7 i x - 7 i (7 i) = 0$

Subtract $7 i x$ from $7 i x$ .

$x \cdot x + 0 - 7 i (7 i) = 0$

Add $x \cdot x$ and $0$ .

$x \cdot x - 7 i (7 i) = 0$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 7 i (7 i) = 0$

Multiply $- 7 i (7 i)$ .

Multiply $7$ by $- 7$ .

$x^{2} - 49 i i = 0$

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

$x^{2} - 49 (i i) = 0$

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

$x^{2} - 49 (i i) = 0$

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

$x^{2} - 49 i^{1 + 1} = 0$

Add $1$ and $1$ .

$x^{2} - 49 i^{2} = 0$

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

$x^{2} - 49 \cdot - 1 = 0$

Multiply $- 49$ by $- 1$ .

$x^{2} + 49 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${7 i, - 7 i}$ is $y = x^{2} + 49$ .

$y = x^{2} + 49$

Step 5

Find the Quadratic Equation 7i , -7i

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