Questions: Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places. x= (smaller value) x= (larger value)

Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
x= (smaller value)
x= (larger value)

Transcript text: Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places. $x=$ $\square$ $\approx$ $\square$ (smaller value) $x=$ $\square$ $\approx$ $\square$ (larger value)

Solution

Solution Steps

To solve the equation by extracting the square roots, we need to isolate the term with the square and then take the square root of both sides. This will give us two solutions: one positive and one negative. We will then calculate both the exact solutions and their approximations rounded to two decimal places.

Step 1: Isolate the Square Term

To solve the equation $x^2 = 25$, we first ensure that the square term is isolated on one side of the equation. In this case, it is already isolated.

Step 2: Extract the Square Roots

Next, we take the square root of both sides of the equation to solve for $x$. This gives us two solutions: \[ x = \sqrt{25} \quad \text{and} \quad x = -\sqrt{25} \]

Step 3: Calculate the Exact Solutions

The exact solutions are: \[ x = 5 \quad \text{and} \quad x = -5 \]

Step 4: Approximate the Solutions

Since the exact solutions are already integers, their approximations to four significant digits are the same: \[ x \approx 5.000 \quad \text{and} \quad x \approx -5.000 \]

Final Answer

$\boxed{x = 5}$ and $\boxed{x = -5}$

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