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What are the solutions of the quadratic equation 49x2 = 9?

x = StartFraction 1 Over 9 EndFraction and x = StartFraction negative 1 Over 9 EndFraction
x = StartFraction 3 Over 7 EndFraction and x = Start Fraction negative 3 Over 7 EndFraction
x = StartFraction 3 Over 4 EndFraction and x = StartFraction negative 3 Over 4 EndFraction
x = StartFraction Over 49 EndFraction and x = StartFraction negative 9 Over 49 EndFraction

1 answer

To solve the quadratic equation \( 49x^2 = 9 \), we start by rearranging it into standard form:

\[ 49x^2 - 9 = 0. \]

Next, we can factor the left-hand side:

\[ (7x - 3)(7x + 3) = 0. \]

Setting each factor equal to zero gives us the solutions:

  1. \( 7x - 3 = 0 \) leads to \( 7x = 3 \) or \( x = \frac{3}{7} \).
  2. \( 7x + 3 = 0 \) leads to \( 7x = -3 \) or \( x = -\frac{3}{7} \).

Thus, the solutions to the equation \( 49x^2 = 9 \) are:

\[ x = \frac{3}{7} \quad \text{and} \quad x = -\frac{3}{7}. \]

Therefore, the correct answer is:

x = Start Fraction 3 Over 7 End Fraction and x = Start Fraction negative 3 Over 7 End Fraction.