To solve this equation, we need to combine like terms and simplify the expression.
First, let's simplify the left side of the equation: 6^x2−4xx^2 - 4xx2−4x + 6^x2−4x−1x^2 - 4x - 1x2−4x−1 = 42 Let a = x^2 - 4x, then the equation becomes: 6^a + 6^a−1a-1a−1 = 42
Now, we can rewrite the equation as: 6^a + 6^a−1a-1a−1 = 6^1 * 7
Next, we can rewrite 6 as 6^1 and simplify: 6^a + 6^a 6^-1 = 6^1 7 6^a + 6^a 1/61/61/6 = 6 7 6^a + 6^a−1a-1a−1 = 42
Now we have simplified the equation and can see that the simplified equation matches the original equation. Therefore, the solution to the equation 6^x2−4xx^2 - 4xx2−4x + 6^x2−4x−1x^2 - 4x - 1x2−4x−1 = 42 is x^2 - 4x = 1.
To solve this equation, we need to combine like terms and simplify the expression.
First, let's simplify the left side of the equation:
6^x2−4xx^2 - 4xx2−4x + 6^x2−4x−1x^2 - 4x - 1x2−4x−1 = 42
Let a = x^2 - 4x, then the equation becomes:
6^a + 6^a−1a-1a−1 = 42
Now, we can rewrite the equation as:
6^a + 6^a−1a-1a−1 = 6^1 * 7
Next, we can rewrite 6 as 6^1 and simplify:
6^a + 6^a 6^-1 = 6^1 7
6^a + 6^a 1/61/61/6 = 6 7
6^a + 6^a−1a-1a−1 = 42
Now we have simplified the equation and can see that the simplified equation matches the original equation. Therefore, the solution to the equation 6^x2−4xx^2 - 4xx2−4x + 6^x2−4x−1x^2 - 4x - 1x2−4x−1 = 42 is x^2 - 4x = 1.