Basic Math Examples

$49 s^{2} + 70 s = - 25$

Step 1

Add $25$ to both sides of the equation.

$49 s^{2} + 70 s + 25 = 0$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $49 s^{2}$ as ${(7 s)}^{2}$ .

${(7 s)}^{2} + 70 s + 25 = 0$

Step 2.2

Rewrite $25$ as $5^{2}$ .

${(7 s)}^{2} + 70 s + 5^{2} = 0$

Step 2.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$70 s = 2 \cdot (7 s) \cdot 5$

Step 2.4

Rewrite the polynomial.

${(7 s)}^{2} + 2 \cdot (7 s) \cdot 5 + 5^{2} = 0$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 7 s$ and $b = 5$ .

${(7 s + 5)}^{2} = 0$

Step 3

Set the $7 s + 5$ equal to $0$ .

$7 s + 5 = 0$

Step 4

Solve for $s$ .

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Step 4.1

Subtract $5$ from both sides of the equation.

$7 s = - 5$

Step 4.2

Divide each term in $7 s = - 5$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 s = - 5$ by $7$ .

$\frac{7 s}{7} = \frac{- 5}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 s}{7} = \frac{- 5}{7}$

Step 4.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 5}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$s = - \frac{5}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{5}{7}$

Decimal Form:

$s = - 0.\overline{714285}$