Basic Math Examples

y^{2} - 6 y = 2

$y^{2} - 6 y = 2$

Step 1

Subtract

2

$2$ from both sides of the equation.

y^{2} - 6 y - 2 = 0

$y^{2} - 6 y - 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

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

Step 3

Substitute the values

a = 1

$a = 1$ ,

b = - 6

$b = - 6$ , and

c = - 2

$c = - 2$ into the quadratic formula and solve for

y

$y$ .

\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot - 2)}}{2 \cdot 1}

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot - 2)}}{2 \cdot 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise

- 6

$- 6$ to the power of

2

$2$ .

y = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

Step 4.1.2

Multiply

- 4 \cdot 1 \cdot - 2

$- 4 \cdot 1 \cdot - 2$ .

Tap for more steps...

Step 4.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

y = \frac{6 \pm \sqrt{36 - 4 \cdot - 2}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{36 - 4 \cdot - 2}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

- 2

$- 2$ .

y = \frac{6 \pm \sqrt{36 + 8}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{36 + 8}}{2 \cdot 1}$

y = \frac{6 \pm \sqrt{36 + 8}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{36 + 8}}{2 \cdot 1}$

Step 4.1.3

Add

36

$36$ and

8

$8$ .

y = \frac{6 \pm \sqrt{44}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{44}}{2 \cdot 1}$

Step 4.1.4

Rewrite

44

$44$ as

2^{2} \cdot 11

$2^{2} \cdot 11$ .

Tap for more steps...

Step 4.1.4.1

Factor

4

$4$ out of

44

$44$ .

y = \frac{6 \pm \sqrt{4 (11)}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{4 (11)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

y = \frac{6 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}$

y = \frac{6 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}

$y = \frac{6 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

y = \frac{6 \pm 2 \sqrt{11}}{2 \cdot 1}

$y = \frac{6 \pm 2 \sqrt{11}}{2 \cdot 1}$

y = \frac{6 \pm 2 \sqrt{11}}{2 \cdot 1}

$y = \frac{6 \pm 2 \sqrt{11}}{2 \cdot 1}$

Step 4.2

Multiply

2

$2$ by

1

$1$ .

y = \frac{6 \pm 2 \sqrt{11}}{2}

$y = \frac{6 \pm 2 \sqrt{11}}{2}$

Step 4.3

Simplify

\frac{6 \pm 2 \sqrt{11}}{2}

$\frac{6 \pm 2 \sqrt{11}}{2}$ .

y = 3 \pm \sqrt{11}

$y = 3 \pm \sqrt{11}$

y = 3 \pm \sqrt{11}

$y = 3 \pm \sqrt{11}$

Step 5

The final answer is the combination of both solutions.

y = 3 + \sqrt{11}, 3 - \sqrt{11}

$y = 3 + \sqrt{11}, 3 - \sqrt{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

y = 3 + \sqrt{11}, 3 - \sqrt{11}

$y = 3 + \sqrt{11}, 3 - \sqrt{11}$

Decimal Form:

y = 6.31662479 \dots, - 0.31662479 \dots

$y = 6.31662479 \dots, - 0.31662479 \dots$