First, distribute on both sides of the equation:
2x^2 - 80 = -x^2 + 6x + 24 + 1
Combine like terms:
2x^2 + x^2 - 6x - 105 = 0
3x^2 - 6x - 105 = 0
Now, this is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. Let's factor it:
3x^2 - 6x - 105 = 03(x^2 - 2x - 35) = 03(x - 7)(x + 5) = 0
Setting each factor to zero:
x - 7 = 0x = 7
x + 5 = 0x = -5
Therefore, the solutions to the equation are x = 7 and x = -5.
First, distribute on both sides of the equation:
2x^2 - 80 = -x^2 + 6x + 24 + 1
Combine like terms:
2x^2 + x^2 - 6x - 105 = 0
3x^2 - 6x - 105 = 0
Now, this is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. Let's factor it:
3x^2 - 6x - 105 = 0
3(x^2 - 2x - 35) = 0
3(x - 7)(x + 5) = 0
Setting each factor to zero:
x - 7 = 0
x = 7
x + 5 = 0
x = -5
Therefore, the solutions to the equation are x = 7 and x = -5.