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\[ x^{2}+10 x+25=0 \] 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.

Ask by Blake Curry. in the United States
Mar 13,2025

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The quadratic equation \( x^{2} + 10x + 25 = 0 \) can be factored as \( (x + 5)^{2} = 0 \).

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The given quadratic equation \( x^{2}+10x+25=0 \) can be factored by recognizing it as a perfect square trinomial. The expression can be rewritten as \( (x+5)(x+5) = (x+5)^{2} \). So, the left-hand side factors to \( (x+5)^{2} = 0 \). Now, if we set the factored form to zero, we find that \( (x+5) = 0 \), leading us to the solution \( x = -5 \). This means the quadratic has one repeated solution, making it a perfect square.

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