Solve for t 7t^2+28t+56=0

$7 t^{2} + 28 t + 56 = 0$

Factor $7$ out of $7 t^{2} + 28 t + 56$ .

Factor $7$ out of $7 t^{2}$ .

$7 (t^{2}) + 28 t + 56 = 0$

Factor $7$ out of $28 t$ .

$7 (t^{2}) + 7 (4 t) + 56 = 0$

Factor $7$ out of $56$ .

$7 t^{2} + 7 (4 t) + 7 \cdot 8 = 0$

Factor $7$ out of $7 t^{2} + 7 (4 t)$ .

$7 (t^{2} + 4 t) + 7 \cdot 8 = 0$

Factor $7$ out of $7 (t^{2} + 4 t) + 7 \cdot 8$ .

$7 (t^{2} + 4 t + 8) = 0$

Divide each term in $7 (t^{2} + 4 t + 8) = 0$ by $7$ and simplify.

Divide each term in $7 (t^{2} + 4 t + 8) = 0$ by $7$ .

$\frac{7 (t^{2} + 4 t + 8)}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (t^{2} + 4 t + 8)}{7} = \frac{0}{7}$

Divide $t^{2} + 4 t + 8$ by $1$ .

$t^{2} + 4 t + 8 = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$t^{2} + 4 t + 8 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 4$ , and $c = 8$ into the quadratic formula and solve for $t$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot 8)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$t = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$t = \frac{- 4 \pm \sqrt{16 - 4 \cdot 8}}{2 \cdot 1}$

Multiply $- 4$ by $8$ .

$t = \frac{- 4 \pm \sqrt{16 - 32}}{2 \cdot 1}$

Subtract $32$ from $16$ .

$t = \frac{- 4 \pm \sqrt{- 16}}{2 \cdot 1}$

Rewrite $- 16$ as $- 1 (16)$ .

$t = \frac{- 4 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$t = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

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

$t = \frac{- 4 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$t = \frac{- 4 \pm i \cdot \sqrt{4^{2}}}{2 \cdot 1}$

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

$t = \frac{- 4 \pm i \cdot 4}{2 \cdot 1}$

Move $4$ to the left of $i$ .

$t = \frac{- 4 \pm 4 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$t = \frac{- 4 \pm 4 i}{2}$

Simplify $\frac{- 4 \pm 4 i}{2}$ .

$t = - 2 \pm 2 i$

The final answer is the combination of both solutions.

$t = - 2 + 2 i, - 2 - 2 i$

Solve for t 7t^2+28t+56=0

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