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Solve for m m^2-10m+25=0

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

Step 1

Factor using the perfect square rule.

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

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

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

$10 m = 2 \cdot m \cdot 5$

Rewrite the polynomial.

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

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

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

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

Step 2

Set the $m - 5$ equal to $0$ .

$m - 5 = 0$

Step 3

Add $5$ to both sides of the equation.

$m = 5$

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