Finite Math Examples

$y^{2} + 2 y - 48 = - 6$

Step 1

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

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Step 1.1

Add $6$ to both sides of the equation.

$y^{2} + 2 y - 48 + 6 = 0$

Step 1.2

Add $- 48$ and $6$ .

$y^{2} + 2 y - 42 = 0$

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 $a = 1$ , $b = 2$ , and $c = - 42$ into the quadratic formula and solve for $y$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 42)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$y = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 42}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 42$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$y = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 42}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 42$ .

$y = \frac{- 2 \pm \sqrt{4 + 168}}{2 \cdot 1}$

Step 4.1.3

Add $4$ and $168$ .

$y = \frac{- 2 \pm \sqrt{172}}{2 \cdot 1}$

Step 4.1.4

Rewrite $172$ as $2^{2} \cdot 43$ .

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Step 4.1.4.1

Factor $4$ out of $172$ .

$y = \frac{- 2 \pm \sqrt{4 (43)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 2 \pm \sqrt{2^{2} \cdot 43}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$y = \frac{- 2 \pm 2 \sqrt{43}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$y = \frac{- 2 \pm 2 \sqrt{43}}{2}$

Step 4.3

Simplify $\frac{- 2 \pm 2 \sqrt{43}}{2}$ .

$y = - 1 \pm \sqrt{43}$

Step 5

The final answer is the combination of both solutions.

$y = - 1 + \sqrt{43}, - 1 - \sqrt{43}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - 1 + \sqrt{43}, - 1 - \sqrt{43}$

Decimal Form:

$y = 5.55743852 \dots, - 7.55743852 \dots$