square root of x^2 -3 =7

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kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

To remove the radical on the left-hand side of the equation, square both sides of the equation.

`(sqrt(x^2-3))^2=(7)^2`

Simplify the right-hand side of the equation.

`x^2-3=49`

Move all terms not containing `x` to the right-hand side of the equation.

`x^2=52`

Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.

`x=+-sqrt(52)`

Simplify the right-hand side of the equation. Reduce the radical prior to substituting in and solving the

`x=+-2 sqrt(13)`

First, substitute in the `+ ` portion of the `+-`  to find the first solution.

`x=2 sqrt(13)`

Next, substitute in the `-` portion of the `+-`  to find the second solution.

`x=-2 sqrt(13)`

The complete solution is the result of both the `+` and `-` portions of the solution.

`x=2 sqrt(13), -2 sqrt(13)`

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Given equation

`sqrt(x^2-3)=7`

To solve , square both side

`x^2-3=49`

`x^2=49+3`

`x^2=52`

`x=+-sqrt(52)`

`` Substitute  `x=sqrt(52)`  and `x=-sqrt(52)`  in given equation,

`sqrt((+-sqrt(52))^2-3)=sqrt(52-3)=sqrt(49)=7`

Thus `x=+-sqrt(52)`  is solution of the given equation.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The equation `sqrt(x^2 -3) =7` has to be solved for x.

`sqrt(x^2 -3) =7`

Square both the sides

`(sqrt(x^2 -3))^2 =7^2`

`x^2 - 3 = 49`

Add 3 to both the sides

`x^2 - 3 + 3 = 49 + 3`

`x^2 = 52`

Now take the square root of both the sides

`sqrt(x^2) = sqrt 52`

`x = +- 2*sqrt 13`

The solution of the equation is `x = +- 2*sqrt 13`

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