To solve the quadratic equation \( 9x^2 = 4 \), we first rewrite it in standard form:
\[ 9x^2 - 4 = 0 \]
Next, we can use the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \( a = 9 \), \( b = 0 \), and \( c = -4 \). Now we can substitute these values into the formula.
First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = 0^2 - 4(9)(-4) = 0 + 144 = 144 \]
Next, we substitute back into the quadratic formula:
\[ x = \frac{-0 \pm \sqrt{144}}{2(9)} = \frac{\pm 12}{18} \]
Simplifying this gives:
\[ x = \frac{12}{18} = \frac{2}{3} \quad \text{and} \quad x = \frac{-12}{18} = -\frac{2}{3} \]
Thus, the solutions to the equation \( 9x^2 = 4 \) are:
\[ x = \frac{2}{3} \quad \text{and} \quad x = -\frac{2}{3} \]
The correct answer is:
x = StartFraction 2 Over 3 EndFraction and x = StartFraction negative 2 Over 3 EndFraction.