Solve for x:
x square root of 3-2=5x square root of 3?
Is the equation
x√3-2=5x√3
or
x(√3-2)=5x√3
or
x√(3-2)=5x√3 ?
The last option is unlikely.
It is the first equation. I did not know how to put the square root sign on the computer.
The square root sign can be made by typing:
& r a d i c ;
without the intervening spaces.
x√3-2=5x√3
regroup terms
5x√3-x√3 = -2
4x√3 = -2
x=-(2/4)/√3
Multiply numerator and denominator by √3 to rationalize the denominator
x=-√3/6
To solve for x in the equation, we need to isolate the variable x. Let's break down the equation step by step:
1. x√3 - 2 = 5x√3
2. First, let's get rid of the square root (√). To do this, we need to square both sides of the equation:
(x√3 - 2)^2 = (5x√3)^2
x√3 * x√3 - 2 * 2√3 + 2 * x√3 - 2 * 2 = 5x√3 * 5x√3
3x^2 - 4√3x + 4 - 4 = 25x^2 * 3
3x^2 - 4√3x - 21x^2 = 0
3. Now, combine like terms:
(3 - 21)x^2 - 4√3x = 0
-18x^2 - 4√3x = 0
4. Factor out the common terms:
-2x(9x + 2√3) = 0
5. Now, we set each factor equal to zero and solve for x:
-2x = 0 --> x = 0
9x + 2√3 = 0
Subtract 2√3 from both sides:
9x = -2√3
Divide both sides by 9:
x = -2√3/9
Therefore, the solutions to the equation are x = 0 and x = -2√3/9.