Basic Math Examples

$- 5 y (1 - 5 y) + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1

Simplify $- 5 y (1 - 5 y) + 5 (- 8 y - 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5 y \cdot 1 - 5 y (- 5 y) + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.2

Multiply $- 5$ by $1$ .

$- 5 y - 5 y (- 5 y) + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$- 5 y - 5 \cdot - 5 y \cdot y + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

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Step 1.1.4.1.1

Move $y$ .

$- 5 y - 5 \cdot - 5 (y \cdot y) + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.4.1.2

Multiply $y$ by $y$ .

$- 5 y - 5 \cdot - 5 y^{2} + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.4.2

Multiply $- 5$ by $- 5$ .

$- 5 y + 25 y^{2} + 5 (- 8 y - 2) = - 4 y - 8 y$

Step 1.1.5

Apply the distributive property.

$- 5 y + 25 y^{2} + 5 (- 8 y) + 5 \cdot - 2 = - 4 y - 8 y$

Step 1.1.6

Multiply $- 8$ by $5$ .

$- 5 y + 25 y^{2} - 40 y + 5 \cdot - 2 = - 4 y - 8 y$

Step 1.1.7

Multiply $5$ by $- 2$ .

$- 5 y + 25 y^{2} - 40 y - 10 = - 4 y - 8 y$

Step 1.2

Subtract $40 y$ from $- 5 y$ .

$25 y^{2} - 45 y - 10 = - 4 y - 8 y$

Step 2

Subtract $8 y$ from $- 4 y$ .

$25 y^{2} - 45 y - 10 = - 12 y$

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

Add $12 y$ to both sides of the equation.

$25 y^{2} - 45 y - 10 + 12 y = 0$

Step 3.2

Add $- 45 y$ and $12 y$ .

$25 y^{2} - 33 y - 10 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 25$ , $b = - 33$ , and $c = - 10$ into the quadratic formula and solve for $y$ .

$\frac{33 \pm \sqrt{{(- 33)}^{2} - 4 \cdot (25 \cdot - 10)}}{2 \cdot 25}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $- 33$ to the power of $2$ .

$y = \frac{33 \pm \sqrt{1089 - 4 \cdot 25 \cdot - 10}}{2 \cdot 25}$

Step 6.1.2

Multiply $- 4 \cdot 25 \cdot - 10$ .

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Step 6.1.2.1

Multiply $- 4$ by $25$ .

$y = \frac{33 \pm \sqrt{1089 - 100 \cdot - 10}}{2 \cdot 25}$

Step 6.1.2.2

Multiply $- 100$ by $- 10$ .

$y = \frac{33 \pm \sqrt{1089 + 1000}}{2 \cdot 25}$

Step 6.1.3

Add $1089$ and $1000$ .

$y = \frac{33 \pm \sqrt{2089}}{2 \cdot 25}$

Step 6.2

Multiply $2$ by $25$ .

$y = \frac{33 \pm \sqrt{2089}}{50}$

Step 7

The final answer is the combination of both solutions.

$y = \frac{33 + \sqrt{2089}}{50}, \frac{33 - \sqrt{2089}}{50}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$y = \frac{33 + \sqrt{2089}}{50}, \frac{33 - \sqrt{2089}}{50}$

Decimal Form:

$y = 1.57411159 \dots, - 0.25411159 \dots$