Question Solve the quadratic equation $(x-16)^{2}=25$ to find the values of $x$ .

Studdy Solution

STEP 1

Assumptions1. We are solving the equation for real numbers.

STEP 2

The given equation is $(x-16)^{2}=25$ . The first step is to take the square root on both sides of the equation. Remember that when we take the square root of a number, we get two values, one positive and one negative.
$\sqrt{(x-16)^{2}} = \pm \sqrt{25}$

STEP 3

implify the equation. The square root of a square is the absolute value of the original number, and the square root of25 is5.
$|x-16| = \pm5$

STEP 4

This equation gives us two separate equations to solve1. $x-16 =$
2. $x-16 = -$

STEP 5

olving the first equation $x-16 =5$ gives $x =16 +5$

STEP 6

Calculate the value of x for the first equation.
$x =16 +5 =21$

STEP 7

olving the second equation $x-16 = -5$ gives $x =16 -5$

STEP 8

Calculate the value of x for the second equation.
$x =16 -5 =11$ So, the solutions to the equation $(x-16)^{2}=25$ are $x =21$ and $x =11$ .

Was this helpful?

Question Solve the quadratic equation $(x-16)^{2}=25$ to find the values of $x$ .

Studdy Solution

STEP 1

Assumptions1. We are solving the equation for real numbers.

STEP 2

The given equation is $(x-16)^{2}=25$ . The first step is to take the square root on both sides of the equation. Remember that when we take the square root of a number, we get two values, one positive and one negative.
$\sqrt{(x-16)^{2}} = \pm \sqrt{25}$

STEP 3

implify the equation. The square root of a square is the absolute value of the original number, and the square root of25 is5.
$|x-16| = \pm5$

STEP 4

This equation gives us two separate equations to solve1. $x-16 =$
2. $x-16 = -$

STEP 5

olving the first equation $x-16 =5$ gives $x =16 +5$

STEP 6

Calculate the value of x for the first equation.
$x =16 +5 =21$

STEP 7

olving the second equation $x-16 = -5$ gives $x =16 -5$

STEP 8

Calculate the value of x for the second equation.
$x =16 -5 =11$ So, the solutions to the equation $(x-16)^{2}=25$ are $x =21$ and $x =11$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Solve the quadratic equation (x−16)2=25(x-16)^{2}=25(x−16)2=25 to find the values of xxx.

Studdy Solution

STEP 1

Assumptions1. We are solving the equation for real numbers.

STEP 2

STEP 3

implify the equation. The square root of a square is the absolute value of the original number, and the square root of25 is5.∣x−16∣=±5|x-16| = \pm5∣x−16∣=±5

STEP 4

This equation gives us two separate equations to solve1. x−16=x-16 =x−16=2. x−16=−x-16 = -x−16=−

STEP 5

olving the first equation x−16=5x-16 =5x−16=5 givesx=16+5x =16 +5x=16+5

STEP 6

Calculate the value of x for the first equation.x=16+5=21x =16 +5 =21x=16+5=21

STEP 7

olving the second equation x−16=−5x-16 = -5x−16=−5 givesx=16−5x =16 -5x=16−5

STEP 8

Calculate the value of x for the second equation.x=16−5=11x =16 -5 =11x=16−5=11So, the solutions to the equation (x−16)2=25(x-16)^{2}=25(x−16)2=25 are x=21x =21x=21 and x=11x =11x=11.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Solve the quadratic equation $(x-16)^{2}=25$ to find the values of $x$ .

implify the equation. The square root of a square is the absolute value of the original number, and the square root of25 is5.
$|x-16| = \pm5$

This equation gives us two separate equations to solve1. $x-16 =$
2. $x-16 = -$

olving the first equation $x-16 =5$ gives $x =16 +5$

Calculate the value of x for the first equation.
$x =16 +5 =21$

olving the second equation $x-16 = -5$ gives $x =16 -5$

Calculate the value of x for the second equation.
$x =16 -5 =11$ So, the solutions to the equation $(x-16)^{2}=25$ are $x =21$ and $x =11$ .