$$ x^{2}+10 x+25=0 $$ Step 1 of 2 : Using the standard form $$ a x^{2}+b x+c=0 $$ of the given quadratic equation, factor the left hand side of the equation into two linear factors.

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To factor the quadratic equation $$ x^{2} + 10x + 25 = 0 $$ into two linear factors, we can follow these steps:

1. **Identify the coefficients**: In the standard form $$ ax^{2} + bx + c = 0 $$, we have:
   - $$ a = 1 $$
   - $$ b = 10 $$
   - $$ c = 25 $$

2. **Look for two numbers that multiply to $$ ac $$ and add to $$ b $$**:
   - Here, $$ ac = 1 \times 25 = 25 $$.
   - We need two numbers that multiply to $$ 25 $$ and add to $$ 10 $$. The numbers $$ 5 $$ and $$ 5 $$ satisfy this condition because:
     - $$ 5 \times 5 = 25 $$
     - $$ 5 + 5 = 10 $$

3. **Write the factors**: Since both numbers are the same, we can write the quadratic as:
   $$
   (x + 5)(x + 5) = (x + 5)^{2}
   $$

Thus, the left-hand side of the equation can be factored as:
$$
(x + 5)^{2} = 0
$$

This is the factorization of the quadratic equation.
The quadratic equation $$ x^{2} + 10x + 25 = 0 $$ can be factored as $$ (x + 5)^{2} = 0 $$.

\[ x^{2}+10 x+25=0 \] Step 1 of 2 : Using the standard form \( a x^{2}+b x+c=0 \) of the given quadratic equation, factor the left hand side of the equation into two linear factors.

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