Question

20 Enter the correct answer in the box. What are the solutions to the equation (x - 21)2 = 25?

Answer 1

The solutions to the equation
`\( (x - 21)^2 = 25 \)` are:

1.
`\( x = 26 \)`

2.
`\( x = 16 \)`

To solve the equation
`\( (x - 21)^2 = 25 \)`, we will use the square root property, which states that if
`\( A^2 = B \)`, then
`\( A = √(B) \)` or
`\( A = -√(B) \)`. Here are the steps for the calculation:

1. Take the square root of both sides of the equation:

`\[ √((x - 21)^2) = \pm √(25) \]`

2. Simplify both sides:

`\[ x - 21 = \pm 5 \]`

3. Solve for
`\( x \)` by adding 21 to both sides of the equation for each case:

`\[ x = 21 \pm 5 \]`

This yields two solutions:

`\[ x = 21 + 5 \]`

`\[ x = 21 - 5 \]`

Now, let's calculate the exact values for \( x \).

The solutions to the equation
`\( (x - 21)^2 = 25 \)` are:

1.
`\( x = 26 \)`

2.
`\( x = 16 \)`

These are the two values of
`\( x \)` when plugged into the equation that will satisfy it.

Answer 2

The given expression is:Given the equation:

`(-(1)/(3))^2+\sqrt[3]{3^4+44}`

The first step is to solve the expression in parentheses, so:

`\begin{gathered} (-(1)/(3))^2=(-(1)/(3))*(-(1)/(3)) \\ \\ \text{ By applying the properties of fractions:} \\ =((-1)*(-1))/(3*3)=(1)/(9) \end{gathered}`

Now, we have:

`(1)/(9)+\sqrt[3]{3^4+44}`

Solve the expression in the root:

`\begin{gathered} 3^4=3*3*3*3=81 \\ 81+44=125 \end{gathered}`

We can rewrite the expression as:

`(1)/(9)+\sqrt[3]{125}\text{ This is the first answer option that is correct}`

Let's continue:

`\begin{gathered} \sqrt[3]{125}=5 \\ \text{ So:} \\ (1)/(9)+5 \end{gathered}`

This is the second answer answer option that is correct.

And finally:

`(1)/(9)+5=((1*1)+(9*5))/(9*1)=(1+45)/(9)=(46)/(9)`

46/9 is the last option that is correct.

`(x-21)^2\text{ = 25}`

Let's simplify the equation to be able to get the solution. We get,

`(x-21)^2\text{ = 25}`