Solve Using the Quadratic Formula d(7d-6)+4=0

$d (7 d - 6) + 4 = 0$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$d (7 d) + d \cdot - 6 + 4 = 0$

Rewrite using the commutative property of multiplication.

$7 d \cdot d + d \cdot - 6 + 4 = 0$

Move $- 6$ to the left of $d$ .

$7 d \cdot d - 6 \cdot d + 4 = 0$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$7 (d \cdot d) - 6 \cdot d + 4 = 0$

Multiply $d$ by $d$ .

$7 d^{2} - 6 \cdot d + 4 = 0$

$7 d^{2} - 6 d + 4 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 7$ , $b = - 6$ , and $c = 4$ into the quadratic formula and solve for $d$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (7 \cdot 4)}}{2 \cdot 7}$

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$d = \frac{6 \pm \sqrt{36 - 4 \cdot 7 \cdot 4}}{2 \cdot 7}$

Multiply $- 4$ by $7$ .

$d = \frac{6 \pm \sqrt{36 - 28 \cdot 4}}{2 \cdot 7}$

Multiply $- 28$ by $4$ .

$d = \frac{6 \pm \sqrt{36 - 112}}{2 \cdot 7}$

Subtract $112$ from $36$ .

$d = \frac{6 \pm \sqrt{- 76}}{2 \cdot 7}$

Rewrite $- 76$ as $- 1 (76)$ .

$d = \frac{6 \pm \sqrt{- 1 \cdot 76}}{2 \cdot 7}$

Rewrite $\sqrt{- 1 (76)}$ as $\sqrt{- 1} \cdot \sqrt{76}$ .

$d = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{76}}{2 \cdot 7}$

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

$d = \frac{6 \pm i \cdot \sqrt{76}}{2 \cdot 7}$

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$d = \frac{6 \pm i \cdot \sqrt{4 (19)}}{2 \cdot 7}$

Rewrite $4$ as $2^{2}$ .

$d = \frac{6 \pm i \cdot \sqrt{2^{2} \cdot 19}}{2 \cdot 7}$

Pull terms out from under the radical.

$d = \frac{6 \pm i \cdot (2 \sqrt{19})}{2 \cdot 7}$

Move $2$ to the left of $i$ .

$d = \frac{6 \pm 2 i \sqrt{19}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$d = \frac{6 \pm 2 i \sqrt{19}}{14}$

Simplify $\frac{6 \pm 2 i \sqrt{19}}{14}$ .

$d = \frac{3 \pm i \sqrt{19}}{7}$

Solve Using the Quadratic Formula d(7d-6)+4=0

Related Questions

Support LCMGCF.com by disabling your adblocker.