To solve this equation, we need to distribute and simplify the terms on the left side:
5 - 3(x - 2(x - 2(x - 2))) = 5 - 3(x - 2(x^2 - 4x + 4)) = 5 - 3(x - 2x^2 + 8x - 8) = 5 - 3x + 6x^2 - 24x + 24 = 6x^2 - 27x + 29 = 2
Now, we have a quadratic equation. Let's set it equal to zero:
6x^2 - 27x + 29 - 2 = 6x^2 - 27x + 27 = 0
Next, let's solve the quadratic equation by using the quadratic formula:
x = (-(-27) ± √((-27)^2 - 4627)) / (2*6x = (27 ± √(729 - 648)) / 1x = (27 ± √81) / 1x = (27 ± 9) / 12
This gives us two solutionsx1 = (27 + 9) / 12 = 36 / 12 = x2 = (27 - 9) / 12 = 18 / 12 = 1.5
Therefore, the solutions to the equation are x = 3 and x = 1.5.
To solve this equation, we need to distribute and simplify the terms on the left side:
5 - 3(x - 2(x - 2(x - 2))) =
5 - 3(x - 2(x^2 - 4x + 4)) =
5 - 3(x - 2x^2 + 8x - 8) =
5 - 3x + 6x^2 - 24x + 24 =
6x^2 - 27x + 29 = 2
Now, we have a quadratic equation. Let's set it equal to zero:
6x^2 - 27x + 29 - 2 =
6x^2 - 27x + 27 = 0
Next, let's solve the quadratic equation by using the quadratic formula:
x = (-(-27) ± √((-27)^2 - 4627)) / (2*6
x = (27 ± √(729 - 648)) / 1
x = (27 ± √81) / 1
x = (27 ± 9) / 12
This gives us two solutions
x1 = (27 + 9) / 12 = 36 / 12 =
x2 = (27 - 9) / 12 = 18 / 12 = 1.5
Therefore, the solutions to the equation are x = 3 and x = 1.5.