What are the solution(s) to the quadratic equation 9x2 = 4?

x = StartFraction 4 Over 9 EndFraction and x = StartFraction negative 4 Over 9 EndFraction
x = StartFraction 2 Over 3 EndFraction and x = StartFraction negative 2 Over 3 EndFraction
x = StartFraction 3 Over 2 EndFraction and x = StartFraction negative 3 Over 2 EndFraction
no real solution

1 answer

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.