Solve Using the Quadratic Formula 49x^2+4=0

$49 x^{2} + 4 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 49$ , $b = 0$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (49 \cdot 4)}}{2 \cdot 49}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 49 \cdot 4}}{2 \cdot 49}$

Multiply $- 4 \cdot 49 \cdot 4$ .

Multiply $- 4$ by $49$ .

$x = \frac{0 \pm \sqrt{0 - 196 \cdot 4}}{2 \cdot 49}$

Multiply $- 196$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 784}}{2 \cdot 49}$

Subtract $784$ from $0$ .

$x = \frac{0 \pm \sqrt{- 784}}{2 \cdot 49}$

Rewrite $- 784$ as $- 1 (784)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 784}}{2 \cdot 49}$

Rewrite $\sqrt{- 1 (784)}$ as $\sqrt{- 1} \cdot \sqrt{784}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{784}}{2 \cdot 49}$

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

$x = \frac{0 \pm i \cdot \sqrt{784}}{2 \cdot 49}$

Rewrite $784$ as $28^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{28^{2}}}{2 \cdot 49}$

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

$x = \frac{0 \pm i \cdot 28}{2 \cdot 49}$

Move $28$ to the left of $i$ .

$x = \frac{0 \pm 28 i}{2 \cdot 49}$

Multiply $2$ by $49$ .

$x = \frac{0 \pm 28 i}{98}$

Simplify $\frac{0 \pm 28 i}{98}$ .

$x = \frac{\pm 2 i}{7}$