Consider an equation of the form x+sqrt(x-a)=b, where a and b are constants. List the steps to solve this problem, explain each step and why you did it.

Question

The equation is x plus square root x-a where x-a is in the square root then =b. 

Answer 1

Assuming you want to solve for x,  you need to get rid of the radicals first.

 

Subtract x to both sides of the equation.

 

√(x - a) = b - x

 

 

Then square both sides of the equation.

 

x - a = (b - x)²

 

x - a = b² - 2bx + x²

 

 

Then move all terms to the right side of the equation.

 

0 = b² + a - 2bx - x + x²

 

0 = x² + (-2b - 1)x + (a + b²)

 

 

You now have a quadratic equation in standard form where

 

A = 1

B = -2b - 1

C = a + b²

 

Use the quadratic formula to solve for x.