Basic Math Examples

$(5 y + 5) (10 y + 5) = 100$

Step 1

Simplify $(5 y + 5) (10 y + 5)$ .

Tap for more steps...

Step 1.1

Expand $(5 y + 5) (10 y + 5)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$5 y (10 y + 5) + 5 (10 y + 5) = 100$

Step 1.1.2

Apply the distributive property.

$5 y (10 y) + 5 y \cdot 5 + 5 (10 y + 5) = 100$

Step 1.1.3

Apply the distributive property.

$5 y (10 y) + 5 y \cdot 5 + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 10 y \cdot y + 5 y \cdot 5 + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2.1.2

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 1.2.1.2.1

Move $y$ .

$5 \cdot 10 (y \cdot y) + 5 y \cdot 5 + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2.1.2.2

Multiply $y$ by $y$ .

$5 \cdot 10 y^{2} + 5 y \cdot 5 + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2.1.3

Multiply $5$ by $10$ .

$50 y^{2} + 5 y \cdot 5 + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2.1.4

Multiply $5$ by $5$ .

$50 y^{2} + 25 y + 5 (10 y) + 5 \cdot 5 = 100$

Step 1.2.1.5

Multiply $10$ by $5$ .

$50 y^{2} + 25 y + 50 y + 5 \cdot 5 = 100$

Step 1.2.1.6

Multiply $5$ by $5$ .

$50 y^{2} + 25 y + 50 y + 25 = 100$

Step 1.2.2

Add $25 y$ and $50 y$ .

$50 y^{2} + 75 y + 25 = 100$

Step 2

Subtract $100$ from both sides of the equation.

$50 y^{2} + 75 y + 25 - 100 = 0$

Step 3

Subtract $100$ from $25$ .

$50 y^{2} + 75 y - 75 = 0$

Step 4

Factor $25$ out of $50 y^{2} + 75 y - 75$ .

Tap for more steps...

Step 4.1

Factor $25$ out of $50 y^{2}$ .

$25 (2 y^{2}) + 75 y - 75 = 0$

Step 4.2

Factor $25$ out of $75 y$ .

$25 (2 y^{2}) + 25 (3 y) - 75 = 0$

Step 4.3

Factor $25$ out of $- 75$ .

$25 (2 y^{2}) + 25 (3 y) + 25 (- 3) = 0$

Step 4.4

Factor $25$ out of $25 (2 y^{2}) + 25 (3 y)$ .

$25 (2 y^{2} + 3 y) + 25 (- 3) = 0$

Step 4.5

Factor $25$ out of $25 (2 y^{2} + 3 y) + 25 (- 3)$ .

$25 (2 y^{2} + 3 y - 3) = 0$

Step 5

Divide each term in $25 (2 y^{2} + 3 y - 3) = 0$ by $25$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $25 (2 y^{2} + 3 y - 3) = 0$ by $25$ .

$\frac{25 (2 y^{2} + 3 y - 3)}{25} = \frac{0}{25}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $25$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{25 (2 y^{2} + 3 y - 3)}{25} = \frac{0}{25}$

Step 5.2.1.2

Divide $2 y^{2} + 3 y - 3$ by $1$ .

$2 y^{2} + 3 y - 3 = \frac{0}{25}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $0$ by $25$ .

$2 y^{2} + 3 y - 3 = 0$

Step 6

Use the quadratic formula to find the solutions.

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

Step 7

Substitute the values $a = 2$ , $b = 3$ , and $c = - 3$ into the quadratic formula and solve for $y$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (2 \cdot - 3)}}{2 \cdot 2}$

Step 8

Simplify.

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Raise $3$ to the power of $2$ .

$y = \frac{- 3 \pm \sqrt{9 - 4 \cdot 2 \cdot - 3}}{2 \cdot 2}$

Step 8.1.2

Multiply $- 4 \cdot 2 \cdot - 3$ .

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $2$ .

$y = \frac{- 3 \pm \sqrt{9 - 8 \cdot - 3}}{2 \cdot 2}$

Step 8.1.2.2

Multiply $- 8$ by $- 3$ .

$y = \frac{- 3 \pm \sqrt{9 + 24}}{2 \cdot 2}$

Step 8.1.3

Add $9$ and $24$ .

$y = \frac{- 3 \pm \sqrt{33}}{2 \cdot 2}$

Step 8.2

Multiply $2$ by $2$ .

$y = \frac{- 3 \pm \sqrt{33}}{4}$

Step 9

The final answer is the combination of both solutions.

$y = - \frac{3 - \sqrt{33}}{4}, - \frac{3 + \sqrt{33}}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{3 - \sqrt{33}}{4}, - \frac{3 + \sqrt{33}}{4}$

Decimal Form:

$y = 0.68614066 \dots, - 2.18614066 \dots$