Solve x^2 = 144 Show your work
To solve the equation x^2 = 144, take the square root of both sides of the equation:
√(x^2) = √144
Since the square root (√) represents both positive and negative solutions, we have:
x = ±√144
x = ±12
Therefore, the solutions to the equation x^2 = 144 are x = 12 and x = -12.
Can you explain this more?
Of course! Let's break it down step by step.
Starting with the equation x^2 = 144, our goal is to find the value(s) of x that satisfy this equation.
To eliminate the square on the left side of the equation, we take the square root of both sides. The square root (√) of a number is the value that, when multiplied by itself, equals the original number.
Taking the square root of x^2, we get:
√(x^2)
Since the square root can represent both positive and negative solutions, we write it as ±√(x^2).
On the right side of the equation, √144 can be simplified to 12. This is because 12 multiplied by itself equals 144.
So, we have:
±√(x^2) = ±12
The ± symbol indicates that there can be both positive and negative solutions.
Next, we can remove the square root notation by squaring both sides of the equation:
(x^2) = 12^2
Squaring 12 gives us 144, so we have:
x^2 = 144
Finally, to solve for x, we take the square root of both sides again:
√(x^2) = √144
Remembering that the square root can represent both positive and negative solutions, we obtain:
x = ±√144
Simplifying √144, we get:
x = ±12
This means that the equation x^2 = 144 has two solutions: x = 12 and x = -12. Both of these values, when squared, will result in 144.
To solve the equation x^2 = 144, you can follow these steps:
Step 1: Recognize that you have a quadratic equation, which means it can be factored.
Step 2: Take the square root of both sides of the equation to eliminate the exponent of 2 on x^2.
√(x^2) = √144
Step 3: Simplify each side of the equation.
x = ±√144
Step 4: Calculate the square root of 144, which is 12.
x = ±12
Therefore, the solution to the equation x^2 = 144 is x = ±12.