To solve these equations, we will first expand the left side of each equation and simplify to form a quadratic equation.
(1) (x-3)^2 - 6 = 2x - 4x^2Expanding (x-3)^2:x^2 - 6x + 9 - 6 = 2x - 4x^2x^2 - 6x + 3 = 2x - 4x^2
Rearranging to set the equation equal to zero:4x^2 + 2x - x^2 - 6x - 3 = 03x^2 - 4x - 3 = 0
(2) (3x + 2)^2 - 3 = 18xExpanding (3x + 2)^2:9x^2 + 12x + 4 - 3 = 18x9x^2 + 12x + 1 = 18x
Rearranging to set the equation equal to zero:9x^2 + 12x + 1 - 18x = 09x^2 - 6x + 1 = 0
Now, we have simplified both equations to quadratic form and can solve for x by factoring or using the quadratic formula.
To solve these equations, we will first expand the left side of each equation and simplify to form a quadratic equation.
(1) (x-3)^2 - 6 = 2x - 4x^2
Expanding (x-3)^2:
x^2 - 6x + 9 - 6 = 2x - 4x^2
x^2 - 6x + 3 = 2x - 4x^2
Rearranging to set the equation equal to zero:
4x^2 + 2x - x^2 - 6x - 3 = 0
3x^2 - 4x - 3 = 0
(2) (3x + 2)^2 - 3 = 18x
Expanding (3x + 2)^2:
9x^2 + 12x + 4 - 3 = 18x
9x^2 + 12x + 1 = 18x
Rearranging to set the equation equal to zero:
9x^2 + 12x + 1 - 18x = 0
9x^2 - 6x + 1 = 0
Now, we have simplified both equations to quadratic form and can solve for x by factoring or using the quadratic formula.