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

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

Step 1

Add $49$ to both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $4$ .

$x = \frac{28 \pm \sqrt{784 - 16 \cdot 49}}{2 \cdot 4}$

Multiply $- 16$ by $49$ .

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

Subtract $784$ from $784$ .

$x = \frac{28 \pm \sqrt{0}}{2 \cdot 4}$

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

$x = \frac{28 \pm \sqrt{0^{2}}}{2 \cdot 4}$

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

$x = \frac{28 \pm 0}{2 \cdot 4}$

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

$x = \frac{28}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{28}{8}$

Cancel the common factor of $28$ and $8$ .

Factor $4$ out of $28$ .

$x = \frac{4 (7)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = \frac{4 \cdot 7}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{4 \cdot 7}{4 \cdot 2}$

Rewrite the expression.

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

Step 5

The final answer is the combination of both solutions.

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