Solve the equation for $x$.
$x^2=16$
Answer (1)
Take the square root of both sides of the equation: x = ± 16 .
Simplify the square root: x = ± 4 .
The solutions are x = 4 and x = − 4 .
The final answer is ± 4 .
Explanation
Understanding the Problem We are given the equation x 2 = 16 and asked to solve for x . This means we need to find all values of x that, when squared, equal 16.
Taking the Square Root To solve the equation x 2 = 16 , we take the square root of both sides. Remember that when taking the square root, we must consider both the positive and negative roots. This is because both a positive number and its negative counterpart, when squared, will result in a positive number.
Simplifying the Square Root Taking the square root of both sides gives us: x = ± 16 Since 16 = 4 , we have: x = ± 4 This means that x can be either 4 or -4.
Final Answer Therefore, the solutions to the equation x 2 = 16 are x = 4 and x = − 4 .
Examples
Understanding how to solve simple quadratic equations like x 2 = 16 is fundamental in many areas of math and science. For example, in physics, if you're analyzing the motion of an object and find that its velocity squared is equal to 16 m 2 / s 2 , solving this equation will tell you the possible speeds of the object (4 m/s and -4 m/s, where the negative indicates direction). This basic skill extends to more complex problems involving energy, projectile motion, and even electrical circuits.
