Answered

Solve for [tex]\(x\)[/tex]:
[tex]\[ 3x = 6x - 2 \][/tex]



Format the following question or task so that it is easier to read.
Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
Do not remove or change LaTeX formatting.
Do not change or remove [tex] [/tex] tags.
If the question is nonsense, rewrite it so that it makes sense.
-----
[tex]$3 x^2+3 y^2=0$[/tex]
-----

Response:
[tex]\[ 3x^2 + 3y^2 = 0 \][/tex]



Answer :

Sure, let's go through the steps to solve the equation [tex]\(3x^2 + 3y^2 = 0\)[/tex]:

1. Divide the Equation by 3:
[tex]\[ 3x^2 + 3y^2 = 0 \][/tex]
Dividing both sides of the equation by 3 simplifies the equation:
[tex]\[ x^2 + y^2 = 0 \][/tex]

2. Analyze the Equation [tex]\(x^2 + y^2 = 0\)[/tex]:
Notice that [tex]\(x^2\)[/tex] and [tex]\(y^2\)[/tex] are both squared terms, which means they are both non-negative (i.e., [tex]\(x^2 \geq 0\)[/tex] and [tex]\(y^2 \geq 0\)[/tex]). The sum of two non-negative terms equals zero only if both terms are zero.

3. Set Each Term to Zero:
Therefore, for the equation [tex]\(x^2 + y^2 = 0\)[/tex] to hold true, both:
[tex]\[ x^2 = 0 \][/tex]
and
[tex]\[ y^2 = 0 \][/tex]

4. Solve for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
If [tex]\(x^2 = 0\)[/tex], then the only solution is:
[tex]\[ x = 0 \][/tex]
Similarly, if [tex]\(y^2 = 0\)[/tex], then the only solution is:
[tex]\[ y = 0 \][/tex]

Therefore, the solution to the equation [tex]\(3x^2 + 3y^2 = 0\)[/tex] is:
[tex]\[ (x, y) = (0, 0) \][/tex]

This means both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] must be zero to satisfy the original equation.