Algebra Examples

$e^{2} - 10 e + 25 = 0$

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$e^{2} - 10 e + 5^{2} = 0$

Step 1.2

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

$10 e = 2 \cdot e \cdot 5$

Step 1.3

Rewrite the polynomial.

$e^{2} - 2 \cdot e \cdot 5 + 5^{2} = 0$

Step 1.4

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

${(e - 5)}^{2} = 0$

Step 2

Simplify ${((2.71828182) - 5)}^{2}$ .

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Step 2.1

Subtract $5$ from $2.71828182$ .

${(- 2.28171817)}^{2} = 0$

Step 2.2

Raise $- 2.28171817$ to the power of $2$ .

$5.20623781 = 0$

Step 3

Since $5.20623781 \neq 0$ , there are no solutions.

No solution