the square root of (x-11) = the square root of (x) - 1
The following equation will require that you square both sides twice before all the radicals are eliminated.
To solve the given equation square root of (x-11) = square root of (x) - 1, follow these steps:
Step 1: Square both sides of the equation.
(x-11) = (x) - 2(square root of x) + 1
Step 2: Simplify the equation by combining like terms.
x - 11 = x - 2(square root of x) + 1
Step 3: Get rid of the square roots by isolating the term with the square root.
x - x - 11 - 1 = -2(square root of x)
Step 4: Simplify the equation further.
-12 = -2(square root of x)
Step 5: Divide both sides of the equation by -2 to solve for the square root of x.
( -12 ) / ( -2 ) = ( -2(square root of x) ) / ( -2 )
Step 6: Simplify the expression by canceling out -2 on the right side.
6 = square root of x
Step 7: Square both sides once more to eliminate the square root.
6^2 = (square root of x)^2
36 = x
So, the solution to the equation is x = 36.
sqrt(x - 11) = sqrt(x) - 1
Well you already have a hint. We square both sides:
x - 11 = x - 2sqrt(x) + 1
Simplify it first. And take all terms with radical sign to the right side of equation:
x - x - 11 - 1 = -2sqrt(x)
-12 = -2sqrt(x)
6 = sqrt(x)
Square both sides for the second time:
x = 36