Problem 3 $c^{2}=4$... [FREE SOLUTION]

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Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 9: Problem 3

$c^{2}=4$

Short Answer

Expert verified

c = \pm 2

Step by step solution

Identify the Equation

First, observe that the equation given is a simple quadratic equation: $c^{2}=4$.

Take the Square Root

To solve for $c$, take the square root of both sides of the equation. The square root of $c^2$ is $c$, and the square root of 4 can be either positive or negative 2: \[c = \pm \sqrt{4}\].

Simplify the Solution

Calculate the square root of 4 to find the values of $c$. Since $\sqrt{4} = 2$, the solutions are: \[c = \pm 2\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Root

To solve a quadratic equation like this one, it鈥檚 important to understand the concept of square roots. The square root of a number is a value that, when multiplied by itself, gives the original number.

For example, the square root of 9 is 3, because 3 multiplied by 3 is 9. Similarly, since 4 = 2 x 2, the square root of 4 is 2.

However, it鈥檚 important to remember that a number can have both a positive and a negative square root. So, the square root of 4 could be either 2 or -2, because both 2 x 2 and (-2) x (-2) result in 4.

Solving Simple Quadratic Equations

A quadratic equation is any equation that can be written in the form ax^2 + bx + c = 0. In this exercise, the quadratic equation is very simple: c^2 = 4.

When you see an equation in this form, the first step is to isolate the variable. Here, the variable is already isolated, so the next step is to solve for the variable by taking the square root of both sides of the equation: c = 卤鈭�4.

Taking the square root means you鈥檙e looking for the number which, when multiplied by itself, equals the given number.

In this case, the square root of c^2 is c, and the square root of 4 is 2 (or -2), as discussed above.

Positive and Negative Solutions

When solving quadratic equations, you will often end up with both positive and negative solutions.

This is because the square root of a number has two values: one positive and one negative.
For instance, in this exercise where c^2 = 4, we determined that the square root of 4 is 2. But remember, -2 is also a square root of 4.

So, when you solve the equation c^2 = 4, you find that c can be either positive 2 or negative 2: c = 卤2.

Therefore, always make sure to consider both the positive and negative solutions when solving quadratic equations. This helps ensure that you have found all possible solutions to the problem.

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91影视

\(c^{2}=4\)

Short Answer

Step by step solution

Identify the Equation

Take the Square Root

Simplify the Solution

Key Concepts

Understanding Square Root

Solving Simple Quadratic Equations

Positive and Negative Solutions

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