Solve Using the Quadratic Formula 4x^2-7x+4=0

$4 x^{2} - 7 x + 4 = 0$

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 $a = 4$ , $b = - 7$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (4 \cdot 4)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 4 \cdot 4}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 16 \cdot 4}}{2 \cdot 4}$

Multiply $- 16$ by $4$ .

$x = \frac{7 \pm \sqrt{49 - 64}}{2 \cdot 4}$

Subtract $64$ from $49$ .

$x = \frac{7 \pm \sqrt{- 15}}{2 \cdot 4}$

Rewrite $- 15$ as $- 1 (15)$ .

$x = \frac{7 \pm \sqrt{- 1 \cdot 15}}{2 \cdot 4}$

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$x = \frac{7 \pm \sqrt{- 1} \cdot \sqrt{15}}{2 \cdot 4}$

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

$x = \frac{7 \pm i \sqrt{15}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{7 \pm i \sqrt{15}}{8}$