Solve the following equation algebraically:
[tex]x^2=36[/tex]
A. [tex]x= \pm 18[/tex]
B. [tex]x= \pm 6[/tex]
C. [tex]x=-6[/tex]
D. [tex]x=-18[/tex]
Answer (2)
The solution to the equation x 2 = 36 is found by taking the square root of both sides, resulting in x = ± 6 . The correct answer corresponds to option B, x = ± 6 .
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Take the square root of both sides of the equation x 2 = 36 .
Simplify the square root to obtain x = ± 6 .
The solutions are x = 6 and x = − 6 .
The correct answer is x = ± 6 , which corresponds to option B. x = ± 6
Explanation
Understanding the Problem We are given the equation x 2 = 36 and asked to solve for x . This means we need to find all values of x that, when squared, equal 36.
Taking the Square Root To solve the equation x 2 = 36 , we take the square root of both sides. Remember that when we take the square root of a number, we need to consider both the positive and negative roots.
Simplifying the Square Root Taking the square root of both sides, we get:
x 2 = ± 36
This simplifies to:
x = ± 6
So, x can be either 6 or -6.
Selecting the Correct Answer Now we compare our solution x = ± 6 with the given options: a. x = ± 18 b. x = ± 6 c. x = − 6 d. x = − 18
Our solution matches option b.
Examples
Understanding how to solve simple quadratic equations like x 2 = 36 is fundamental in many areas of math and science. For example, if you are designing a square garden with an area of 36 square meters, you need to solve this equation to find the length of each side. Similarly, in physics, if you are calculating the velocity of an object based on its kinetic energy, you might encounter a similar equation. Knowing how to solve these equations quickly and accurately is a valuable skill.
