Now we have the equation x^2 - 8x + 15 = 3x - 15. Rearranging terms gives us: x^2 - 11x + 30 = 0
Solve the equation 10x = 12: Divide by 10 on both sides to isolate x: x = 12/10 = 6/5 = 1.2
Expand and simplify the expression 4(4x-2) = 4x-2: 4(4x-2) = 16x - 8
Solve the equation 2x^6 - 11x - 40 = 0: This is a sixth-degree polynomial equation and can be solved through factoring or using numerical methods such as the rational root theorem or graphing the function.
To solve each of these equations, we will take the steps needed for each one:
Expand and simplify the expression (x-3)(x-5) = 3(x-5):(x-3)(x-5) = x^2 - 5x - 3x + 15 = x^2 - 8x + 15
3(x-5) = 3x - 15
Now we have the equation x^2 - 8x + 15 = 3x - 15.
Rearranging terms gives us:
x^2 - 11x + 30 = 0
Solve the equation 10x = 12:
Divide by 10 on both sides to isolate x:
x = 12/10 = 6/5 = 1.2
Expand and simplify the expression 4(4x-2) = 4x-2:
4(4x-2) = 16x - 8
Solve the equation 2x^6 - 11x - 40 = 0:
This is a sixth-degree polynomial equation and can be solved through factoring or using numerical methods such as the rational root theorem or graphing the function.
Expand and simplifying the expression (x-3)(x-2) = 6(x-3):
(x-3)(x-2) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6
6(x-3) = 6x - 18
Now we have the equation x^2 - 5x + 6 = 6x - 18.
Rearranging terms gives us:
x^2 - 11x + 24 = 0
These are the solutions for the equations provided.