Linear Algebra Examples

$1.3 = (4.2) t + 0.5 (- 9.8) t^{2}$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the right side.

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Step 1.1.1

Multiply $0.5$ by $- 9.8$ .

$1.3 = 4.2 t - 4.9 t^{2}$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Subtract $4.2 t$ from both sides of the equation.

$1.3 - 4.2 t = - 4.9 t^{2}$

Step 1.2.2

Add $4.9 t^{2}$ to both sides of the equation.

$1.3 - 4.2 t + 4.9 t^{2} = 0$

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 $a = 4.9$ , $b = - 4.2$ , and $c = 1.3$ into the quadratic formula and solve for $t$ .

$\frac{4.2 \pm \sqrt{{(- 4.2)}^{2} - 4 \cdot (4.9 \cdot 1.3)}}{2 \cdot 4.9}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 4.2$ to the power of $2$ .

$t = \frac{4.2 \pm \sqrt{17.64 - 4 \cdot 4.9 \cdot 1.3}}{2 \cdot 4.9}$

Step 4.1.2

Multiply $- 4 \cdot 4.9 \cdot 1.3$ .

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Step 4.1.2.1

Multiply $- 4$ by $4.9$ .

$t = \frac{4.2 \pm \sqrt{17.64 - 19.6 \cdot 1.3}}{2 \cdot 4.9}$

Step 4.1.2.2

Multiply $- 19.6$ by $1.3$ .

$t = \frac{4.2 \pm \sqrt{17.64 - 25.48}}{2 \cdot 4.9}$

Step 4.1.3

Subtract $25.48$ from $17.64$ .

$t = \frac{4.2 \pm \sqrt{- 7.84}}{2 \cdot 4.9}$

Step 4.1.4

Rewrite $- 7.84$ as $- 1 (7.84)$ .

$t = \frac{4.2 \pm \sqrt{- 1 \cdot 7.84}}{2 \cdot 4.9}$

Step 4.1.5

Rewrite $\sqrt{- 1 (7.84)}$ as $\sqrt{- 1} \cdot \sqrt{7.84}$ .

$t = \frac{4.2 \pm \sqrt{- 1} \cdot \sqrt{7.84}}{2 \cdot 4.9}$

Step 4.1.6

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

$t = \frac{4.2 \pm i \cdot \sqrt{7.84}}{2 \cdot 4.9}$

Step 4.1.7

Rewrite $7.84$ as ${2.8}^{2}$ .

$t = \frac{4.2 \pm i \cdot \sqrt{{2.8}^{2}}}{2 \cdot 4.9}$

Step 4.1.8

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

$t = \frac{4.2 \pm i \cdot 2.8}{2 \cdot 4.9}$

Step 4.1.9

Move $2.8$ to the left of $i$ .

$t = \frac{4.2 \pm 2.8 i}{2 \cdot 4.9}$

Step 4.2

Multiply $2$ by $4.9$ .

$t = \frac{4.2 \pm 2.8 i}{9.8}$

Step 4.3

Multiply by $1$ .

$t = \frac{1 (4.2 \pm 2.8 i)}{9.8}$

Step 4.4

Factor $9.8$ out of $9.8$ .

$t = \frac{1 (4.2 \pm 2.8 i)}{9.8 (1)}$

Step 4.5

Separate fractions.

$t = \frac{1}{9.8} \cdot \frac{4.2 \pm 2.8 i}{1}$

Step 4.6

Divide $1$ by $9.8$ .

$t = 0.10204081 (\frac{4.2 \pm 2.8 i}{1})$

Step 4.7

Divide $4.2 \pm 2.8 i$ by $1$ .

$t = 0.10204081 (4.2 \pm 2.8 i)$