Finite Math Examples

$y^{2} - 2 y + 1 y = 101 y$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $y^{2} - 2 y + 1 y$ .

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Step 1.1.1.1

Multiply $y$ by $1$ .

$y^{2} - 2 y + y = 101 y$

Step 1.1.1.2

Add $- 2 y$ and $y$ .

$y^{2} - y = 101 y$

Step 1.2

Subtract $101 y$ from both sides of the equation.

$y^{2} - y - 101 y = 0$

Step 1.3

Subtract $101 y$ from $- y$ .

$y^{2} - 102 y = 0$

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 $a = 1$ , $b = - 102$ , and $c = 0$ into the quadratic formula and solve for $y$ .

$\frac{102 \pm \sqrt{{(- 102)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 102$ to the power of $2$ .

$y = \frac{102 \pm \sqrt{10404 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 0$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$y = \frac{102 \pm \sqrt{10404 - 4 \cdot 0}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $0$ .

$y = \frac{102 \pm \sqrt{10404 + 0}}{2 \cdot 1}$

Step 4.1.3

Add $10404$ and $0$ .

$y = \frac{102 \pm \sqrt{10404}}{2 \cdot 1}$

Step 4.1.4

Rewrite $10404$ as $102^{2}$ .

$y = \frac{102 \pm \sqrt{102^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$y = \frac{102 \pm 102}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$y = \frac{102 \pm 102}{2}$

Step 4.3

Simplify $\frac{102 \pm 102}{2}$ .

$y = 51 \pm 51$

Step 5

The final answer is the combination of both solutions.

$y = 102, 0$