Solve quadratic equation. 9x^{2}+6x+1=0

Question

Solve quadratic equation.

9 x^{2} + 6 x + 1 = 0

Answer 1

Step 1
Consider the given equation.

9 x^{2} + 6 x + 1 = 0

Now, find the factor of the equation.

9 x^{2} + 6 x + 1 = 0

9 x^{2} + 3 x + 3 x + 1 = 0

3x(3x+1)+1(3x+1)=0

{(3 x + 1)}^{2} = 0

Step 2
Further simplify.
(3x+1)=0
3x=-1

x = - \frac{1}{3}

Therefore, the solution of the equation is

x = - \frac{1}{3}

.

Answer 2

Step 1: Use the formula for the roots of the quadratic equation

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

In the standard form, determine a, b and c from the original equation and insert them into the formula for the roots of the quadratic equation.

9 x^{2} + 6 x + 1 = 0

a=9
b=6
c=1

x = \frac{- 6 \pm \sqrt{6^{2} - 4 \cdot 9 \cdot 1}}{2 \cdot 9}

Step 2: Raise to the degree

x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 9 \cdot 1}}{2 \cdot 9}

x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 9 \cdot 1}}{2 \cdot 9}

Step 3: Multiply the numbers

x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 9 \cdot 1}}{2 \cdot 9}

x = \frac{- 6 \pm \sqrt{36 - 36}}{2 \cdot 9}

Step 4: Subtract the numbers

x = \frac{- 6 \pm \sqrt{36 - 36}}{2 \cdot 9}

x = \frac{- 6 \pm \sqrt{0}}{2 \cdot 9}

Step 5: Calculate the square root

x = \frac{- 6 \pm \sqrt{0}}{2 \cdot 9}

x = \frac{- 6 \pm 0}{2 \cdot 9}

Step 6: Add zero

x = \frac{- 6 \pm 0}{2 \cdot 9}

x = \frac{- 6}{2 \cdot 9}

Step 7: Multiply the numbers

x = \frac{- 6}{2 \cdot 9}

x = \frac{- 6}{18}

Step 8: Reduce the same terms in the numerator and denominator

x = \frac{- 6}{18}

x = - \frac{1}{3}

The solution

x = - \frac{1}{3}

Expert Answer