Question

Решить уравнение (x-3)^2-(x+1)^2=12

Answer 1

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Answer 2

To solve the equation $(x-3)^2 - (x+1)^2 = 12$, we can first simplify the left-hand side of the equation using algebraic manipulation, and then solve for $x$. Let's proceed step by step:

Step 1: Expand the squared terms. $(x-3)^2 - (x+1)^2 = (x^2 - 6x + 9) - (x^2 + 2x + 1) = x^2 - 6x + 9 - x^2 - 2x - 1$

Step 2: Combine like terms. $x^2 - x^2 - 6x - 2x + 9 - 1 = -8x + 8$

Now the equation becomes: $-8x + 8 = 12$

Step 3: Isolate the variable $x$. Subtract 8 from both sides of the equation: $-8x = 12 - 8$ $-8x = 4$

Step 4: Solve for $x$. Divide both sides by -8 to solve for $x$: $x = \frac{4}{-8}$ $x = -\frac{1}{2}$

So the solution to the equation is $x = -\frac{1}{2}$.