Questions: Solve the equation for all values of (x). [49 x^2-144=0]

Solution Steps

To solve the equation \(49x^2 - 144 = 0\), we can follow these steps:

1. Recognize that this is a quadratic equation in the form \(ax^2 + bx + c = 0\).
2. Move the constant term to the other side of the equation to isolate the quadratic term.
3. Solve for \(x\) by taking the square root of both sides.

The given equation is: \[ 49x^2 - 144 = 0 \]

Move the constant term to the other side of the equation: \[ 49x^2 = 144 \]

Divide both sides by 49: \[ x^2 = \frac{144}{49} \]

Take the square root of both sides: \[ x = \pm \sqrt{\frac{144}{49}} \]

Calculate the square root: \[ x = \pm \frac{\sqrt{144}}{\sqrt{49}} = \pm \frac{12}{7} \]

Final Answer