Questions: Solve (x-3)^2=5 A. x=5 ± √3 B. x=3 ± √5 C. x=-3 ± √5 D. x=8 and x=-2

Transcript text: Solve $(x-3)^{2}=5$ A. $x=5 \pm \sqrt{3}$ B. $x=3 \pm \sqrt{5}$ C. $x=-3 \pm \sqrt{5}$ D. $x=8$ and $x=-2$

Solution

Solution Steps

To solve the equation $(x-3)^{2}=5$, we need to take the square root of both sides to isolate $x$. This will give us two possible solutions for $x$, since taking the square root can yield both a positive and a negative result. After taking the square root, we solve for $x$ by adding 3 to both sides.

Step 1: Isolate the Square

We start with the equation $(x-3)^2 = 5$. To solve for $x$, we first take the square root of both sides, which gives us two possible equations: \[ x - 3 = \sqrt{5} \] \[ x - 3 = -\sqrt{5} \]

Step 2: Solve for $x$

Next, we solve each equation for $x$.

For the first equation: \[ x = 3 + \sqrt{5} \]

For the second equation: \[ x = 3 - \sqrt{5} \]

Step 3: Calculate the Values

We calculate the numerical values of the solutions using $\sqrt{5} \approx 2.2361$.

For $x = 3 + \sqrt{5}$: \[ x \approx 3 + 2.2361 = 5.2361 \]

For $x = 3 - \sqrt{5}$: \[ x \approx 3 - 2.2361 = 0.7639 \]