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Question
x^{2}+6x+9=0
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
More methods
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x=-3
Evaluate
x^{2}+6x+9=0
\text{Use }a^2+2ab+b^2=(a+b)^2\text{ to factor the expression}
\left(x+3\right)^{2}=0
Simplify the expression
x+3=0
Move the constant to the right-hand side and change its sign
x=0-3
Solution
x=-3
x=-3
Evaluate
x^{2}+6x+9=0
\text{Substitute a=}1\text{,b=}6\text{ and c=}9\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{-6\pm \sqrt{6^{2}-4\times 9}}{2}
Simplify the expression
More Steps
Evaluate
6^{2}-4\times 9
Multiply the numbers
6^{2}-36
Simplify
36-36
Calculate
0
x=\frac{-6\pm \sqrt{0}}{2}
Simplify the radical expression
x=\frac{-6\pm 0}{2}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{-6+0}{2}\\&x=\frac{-6-0}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{-6+0}{2}
Simplify
More Steps
Evaluate
\frac{-6+0}{2}
Removing 0 doesn't change the value,so remove it from the expression
\frac{-6}{2}
Reduce the numbers
\frac{-3}{1}
Calculate
-3
x=-3
\begin{align}&x=-3\\&x=\frac{-6-0}{2}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{-6-0}{2}
Simplify
More Steps
Evaluate
\frac{-6-0}{2}
Removing 0 doesn't change the value,so remove it from the expression
\frac{-6}{2}
Reduce the numbers
\frac{-3}{1}
Calculate
-3
x=-3
\begin{align}&x=-3\\&x=-3\end{align}
Solution
x=-3
x=-3
Evaluate
x^{2}+6x+9=0
Add or subtract both sides
x^{2}+6x=-9
Add the same value to both sides
x^{2}+6x+9=-9+9
Simplify the expression
\left(x+3\right)^{2}=0
Simplify the expression
x+3=0
Move the constant to the right-hand side and change its sign
x=0-3
Solution
x=-3
x=-3
Evaluate
x^{2}+6x+9=0
Solve using the PQ formula
x=-\frac{6}{2}\pm \sqrt{\left(\frac{6}{2}\right)^{2}-9}
Simplify the expression
More Steps
Evaluate
\left(\frac{6}{2}\right)^{2}-9
Divide the terms
More Steps
Evaluate
\frac{6}{2}
Reduce the numbers
\frac{3}{1}
Calculate
3
3^{2}-9
Simplify
9-9
Calculate
0
x=-\frac{6}{2}\pm \sqrt{0}
Simplify the expression
x=-\frac{6}{2}\pm 0
Divide the terms
x=-3\pm 0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=-3+0\\&x=-3-0\end{align}
Removing 0 doesn't change the value,so remove it from the expression
\begin{align}&x=-3\\&x=-3-0\end{align}
Removing 0 doesn't change the value,so remove it from the expression
\begin{align}&x=-3\\&x=-3\end{align}
Solution
x=-3
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