Question

What is the solution to √4x-64=6? Show your work.

Answer 1

Hello!

Answer:

`\Large \boxed{\text{If the equation is} ~\sf √(4x) -64=6 ~~~~~~x = 1225}`

`\Large \boxed{\text{If the equation is} ~\sf \sf √(4x-64) =6 ~~~~~~x = 25}`

Explanation:

We have two equations possible:

`\sf √(4x) -64=6`

or

`\sf √(4x-64) =6`

First equation:

We want to solve:

`\sf √(4x) -64=6`

◼ Add 64 from both sides:

`\sf √(4x) -64 + 64 = 6+64`

◼ Simplify both sides:

`\sf √(4x) = 70`

◼ We know that √x² = x, so:

`\sf (√(4x) ) ^2 = 70^2`

◼ Simplify both sides:

`\sf 4x =4900`

Divide both sides by 4:

`\sf (4x)/(4) =(4900)/(4)`

◼ Simplify both sides:

`\boxed{\sf x =1225}`

Second equation:

We want to solve:

`\sf √(4x-64) =6`

◼ We know that √x² = x, so:

`\sf (√(4x-64))^2 =6^2`

◼ Simplify both sides:

`\sf 4x-64 =36`

◼ Add 64 from both sides:

`\sf 4x-64 +64=36+64`

◼ Simplify both sides:

`\sf 4x=100`

Divide both sides by 4:

`\sf (4x)/(4) =(100)/(4)`

◼ Simplify both sides:

`\boxed{\sf x =25}`