Solve Using the Quadratic Formula 9x^2+6x+1=0

Problem

$9x^2+6x+1=0$

Solution

1. Identify the coefficients $a$ $b$ and $c$ from the quadratic equation in the form $a{x}^2+bx+c=0$

$a=9$

$b=6$

$c=1$

2. State the quadratic formula used to find the roots of the equation.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

3. Substitute the values of $a$ $b$ and $c$ into the formula.

$x=\frac{-6\pm \sqrt{6^2-4\left(9\right)\left(1\right)}}{2\left(9\right)}$

4. Simplify the expression inside the square root, which is the discriminant.

$x=\frac{-6\pm \sqrt{36-36}}{18}$

$x=\frac{-6\pm \sqrt{0}}{18}$

5. Calculate the final value for $x$ since the discriminant is zero, indicating one real repeated root.

$x=\frac{-6}{18}$

$x=-\frac{1}{3}$

Final Answer

$x=-\frac{1}{3}$

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