/6x^2-2=2-x
/=radical sign
Is all of 6x^2 -2 under the radical sign?
If so, square both sides, combine terms and solve.
6x^2 -2 = 4 -4x +x^2
5x^2 +4x -6 = 0
That does not factor easily. Use the quadratic equation if you want to solve for the two x roots.
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It creates unnecessary work for the tutors.
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simplified x/2-1/3=1/2
To solve the equation /6x^2 - 2 = 2 - x, we first need to remove the radical sign (/).
Here's how you can solve this equation step by step:
1. Start by isolating the radical (/) term on one side. In this case, we want to get rid of the /6x^2 on the left side. To do that, we need to square both sides of the equation:
(/6x^2)^2 = (2 - x)^2
Simplifying, we have:
6x^2 = (2 - x)^2
2. Expand the squared term on the right side:
6x^2 = (2 - x)(2 - x)
6x^2 = 4 - 2x - 2x + x^2
6x^2 = 4 - 4x + x^2
3. Rearrange the equation to form a quadratic equation:
6x^2 - x^2 - 4x + 4 = 0
4. Combine like terms and simplify:
5x^2 - 4x + 4 = 0
Now, you can either factor, complete the square, or use the quadratic formula to solve for x. The quadratic formula is generally the most reliable method. However, let's factor this equation to find the solutions:
5. To factor the quadratic equation, we look for two numbers that multiply to give 20 (the product of the coefficient of x^2 and the constant term) and add up to give -4 (the coefficient of the linear term):
(5x - 2)(x - 2) = 0
6. Now, set each factor equal to zero and solve for x:
5x - 2 = 0 or x - 2 = 0
Solving each equation:
5x = 2 or x = 2
Dividing both sides by 5:
x = 2/5 or x = 2
So, the solutions to the equation /6x^2 - 2 = 2 - x are x = 2/5 and x = 2.