Question
Consider the following quadratic equation: \[ x^{2}+10 x+25=0 \] Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
Ask by Campbell Williams. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -5 \)
Solution
Solve the equation \( x^{2}+10x+25=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}+10x+25=0\)
- step1: Factor the expression:
\(\left(x+5\right)^{2}=0\)
- step2: Simplify the expression:
\(x+5=0\)
- step3: Move the constant to the right side:
\(x=0-5\)
- step4: Remove 0:
\(x=-5\)
The solution to the quadratic equation \(x^{2}+10x+25=0\) by factoring is \(x=-5\).
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Simplify this solution Beyond the Answer
To solve the quadratic equation \( x^{2}+10 x+25=0 \) by factoring, we first notice that it can be rewritten as \( (x + 5)(x + 5) = 0 \) or \( (x + 5)^2 = 0 \). This tells us that the equation has a double root. To find the value of \( x \), we set \( (x + 5) = 0 \). Therefore, \( x = -5 \). Thus, the solution to the equation is \( x = -5 \).
