Solve Using the Quadratic Formula 49x^2+4=28x

$49 x^{2} + 4 = 28 x$

Step 1

Subtract $28 x$ from both sides of the equation.

$49 x^{2} + 4 - 28 x = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 49$ , $b = - 28$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{28 \pm \sqrt{{(- 28)}^{2} - 4 \cdot (49 \cdot 4)}}{2 \cdot 49}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 28$ to the power of $2$ .

$x = \frac{28 \pm \sqrt{784 - 4 \cdot 49 \cdot 4}}{2 \cdot 49}$

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

Multiply $- 4$ by $49$ .

$x = \frac{28 \pm \sqrt{784 - 196 \cdot 4}}{2 \cdot 49}$

Multiply $- 196$ by $4$ .

$x = \frac{28 \pm \sqrt{784 - 784}}{2 \cdot 49}$

Subtract $784$ from $784$ .

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

Rewrite $0$ as $0^{2}$ .

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

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

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

$28$ plus or minus $0$ is $28$ .

$x = \frac{28}{2 \cdot 49}$

Multiply $2$ by $49$ .

$x = \frac{28}{98}$

Cancel the common factor of $28$ and $98$ .

Factor $14$ out of $28$ .

$x = \frac{14 (2)}{98}$

Cancel the common factors.

Factor $14$ out of $98$ .

$x = \frac{14 \cdot 2}{14 \cdot 7}$

Cancel the common factor.

$x = \frac{14 \cdot 2}{14 \cdot 7}$

Rewrite the expression.

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

Step 5

The final answer is the combination of both solutions.

$x = \frac{2}{7}$ Double roots