Solve Using the Quadratic Formula x^2+4=0

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Algebra

$x^{2} + 4 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = 0$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 4)}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16}}{2 \cdot 1}$

Subtract $16$ from $0$ .

$x = \frac{0 \pm \sqrt{- 16}}{2 \cdot 1}$

Rewrite $- 16$ as $- 1 (16)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{4^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm i \cdot 4}{2 \cdot 1}$

Move $4$ to the left of $i$ .

$x = \frac{0 \pm 4 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4 i}{2}$

Simplify $\frac{0 \pm 4 i}{2}$ .

$x = \pm 2 i$

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Name

Name	nine hundred forty-two million five hundred ninety-five thousand nine hundred thirty-two

Interesting facts

942595932 has 64 divisors, whose sum is 2969032320
The reverse of 942595932 is 239595249
Previous prime number is 67

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 48
Digital Root 3

Name

Name	one billion five hundred twenty-two million one hundred ninety thousand six hundred sixty-seven

Interesting facts

1522190667 has 8 divisors, whose sum is 2048556096
The reverse of 1522190667 is 7660912251
Previous prime number is 107

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	forty-six million six hundred fifty-two thousand four hundred fifty-two

Interesting facts

46652452 has 64 divisors, whose sum is 131798016
The reverse of 46652452 is 25425664
Previous prime number is 167

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 34
Digital Root 7

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