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

Solve the equation for all values of (x). [49 x^2-144=0]
Transcript text: Question Solve the equation for all values of $x$. \[ 49 x^{2}-144=0 \] Answer Attempt 2 out of 2
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Solution

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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.
Step 1: Recognize the Quadratic Equation

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

Step 2: Isolate the Quadratic Term

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

Step 3: Solve for \(x\)

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

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

Step 4: Simplify the Square Root

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

Final Answer

\[ \boxed{x = \pm 1.714} \]

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