- Divide both sides of the equation \(7x^2 = 1008\) by \(7\) to obtain \(x^2 = 144\).
- Calculate the square root of \(144\) to solve for \(x\), which gives \(x = \pm 12\).
- Identify that the correct choice from the provided options is B.
- Final Answer: \(\boxed{\pm 12}\)
Explanation
- Problem Analysis and Method Selection
The goal is to solve the quadratic equation \(7x^2 = 1008\) by following a specific two-step method. This method involves isolating the \(x^2\) term by dividing both sides of the equation by the coefficient of \(x^2\), and then solving for \(x\) by taking the square root of both sides. This approach is effective for equations in the form \(ax^2 = b\).
- Isolating the Squared Term
The first step is to isolate \(x^2\). We have the equation:
\[7x^2 = 1008\]
Dividing both sides by \(7\), we get:
\[x^2 = \frac{1008}{7}\]
Performing the division:
\[1008 \div 7 = 144\]
Thus, the equation simplifies to:
\[x^2 = 144\]
- Solving for x and Selecting the Final Option
Now that we have \(x^2 = 144\), we take the square root of both sides to solve for \(x\).
\[x = \pm\sqrt{144}\]
Since \(12 \times 12 = 144\), the square root of \(144\) is \(12\). Therefore:
\[x = \pm 12\]
Comparing this result to the given options, we find that the solution matches option B.
Examples
Quadratic equations like this are frequently used in physics and geometry. For instance, if you know the area of a square is \(1008\) square units and it is scaled by a factor of \(7\), you can use this method to determine the side length. Similarly, when calculating the time it takes for an object to fall a certain distance under gravity, you encounter similar equations where finding the square root is essential to determine the elapsed time. Mastery of this algebraic technique allows for efficient solving of many such real-world problems.