Solve Using the Quadratic Formula 49x^2+25=70x

$49 x^{2} + 25 = 70 x$

Step 1

Subtract $70 x$ from both sides of the equation.

$49 x^{2} + 25 - 70 x = 0$

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 $a = 49$ , $b = - 70$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{70 \pm \sqrt{{(- 70)}^{2} - 4 \cdot (49 \cdot 25)}}{2 \cdot 49}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 70$ to the power of $2$ .

$x = \frac{70 \pm \sqrt{4900 - 4 \cdot 49 \cdot 25}}{2 \cdot 49}$

Multiply $- 4 \cdot 49 \cdot 25$ .

Multiply $- 4$ by $49$ .

$x = \frac{70 \pm \sqrt{4900 - 196 \cdot 25}}{2 \cdot 49}$

Multiply $- 196$ by $25$ .

$x = \frac{70 \pm \sqrt{4900 - 4900}}{2 \cdot 49}$

Subtract $4900$ from $4900$ .

$x = \frac{70 \pm \sqrt{0}}{2 \cdot 49}$

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

$x = \frac{70 \pm \sqrt{0^{2}}}{2 \cdot 49}$

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

$x = \frac{70 \pm 0}{2 \cdot 49}$

$70$ plus or minus $0$ is $70$ .

$x = \frac{70}{2 \cdot 49}$

Multiply $2$ by $49$ .

$x = \frac{70}{98}$

Cancel the common factor of $70$ and $98$ .

Factor $14$ out of $70$ .

$x = \frac{14 (5)}{98}$

Cancel the common factors.

Factor $14$ out of $98$ .

$x = \frac{14 \cdot 5}{14 \cdot 7}$

Cancel the common factor.

$x = \frac{14 \cdot 5}{14 \cdot 7}$

Rewrite the expression.

$x = \frac{5}{7}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{7}$ Double roots