Basic Math Examples

$s^{2} + 8 s + 3 = 2 s^{2} + 2 s - 1$

Step 1

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

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Step 1.1

Subtract $2 s^{2}$ from both sides of the equation.

$s^{2} + 8 s + 3 - 2 s^{2} = 2 s - 1$

Step 1.2

Subtract $2 s$ from both sides of the equation.

$s^{2} + 8 s + 3 - 2 s^{2} - 2 s = - 1$

Step 1.3

Subtract $2 s^{2}$ from $s^{2}$ .

$- s^{2} + 8 s + 3 - 2 s = - 1$

Step 1.4

Subtract $2 s$ from $8 s$ .

$- s^{2} + 6 s + 3 = - 1$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$- s^{2} + 6 s + 3 + 1 = 0$

Step 2.2

Add $3$ and $1$ .

$- s^{2} + 6 s + 4 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = - 1$ , $b = 6$ , and $c = 4$ into the quadratic formula and solve for $s$ .

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

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $6$ to the power of $2$ .

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

Step 5.1.2

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

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Step 5.1.2.1

Multiply $- 4$ by $- 1$ .

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

Step 5.1.2.2

Multiply $4$ by $4$ .

$s = \frac{- 6 \pm \sqrt{36 + 16}}{2 \cdot - 1}$

Step 5.1.3

Add $36$ and $16$ .

$s = \frac{- 6 \pm \sqrt{52}}{2 \cdot - 1}$

Step 5.1.4

Rewrite $52$ as $2^{2} \cdot 13$ .

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Step 5.1.4.1

Factor $4$ out of $52$ .

$s = \frac{- 6 \pm \sqrt{4 (13)}}{2 \cdot - 1}$

Step 5.1.4.2

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

$s = \frac{- 6 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot - 1}$

Step 5.1.5

Pull terms out from under the radical.

$s = \frac{- 6 \pm 2 \sqrt{13}}{2 \cdot - 1}$

Step 5.2

Multiply $2$ by $- 1$ .

$s = \frac{- 6 \pm 2 \sqrt{13}}{- 2}$

Step 5.3

Simplify $\frac{- 6 \pm 2 \sqrt{13}}{- 2}$ .

$s = 3 \pm \sqrt{13}$

Step 6

The final answer is the combination of both solutions.

$s = 3 + \sqrt{13}, 3 - \sqrt{13}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = 3 + \sqrt{13}, 3 - \sqrt{13}$

Decimal Form:

$s = 6.60555127 \dots, - 0.60555127 \dots$