Now, we have a quadratic equation to solve. We can either use the quadratic formula or factorization method to find the values of x. Let's use the quadratic formula:
x = (-(-7) ± √((-7)^2 - 43.53)) / 2*3.5 x = (7 ± √(49 - 42)) / 7 x = (7 ± √7) / 7 x = (7 ± √7) / 7
Therefore, the solutions for the equation are x = (7 + √7) / 7 and x = (7 - √7) / 7.
To solve this equation, we will first distribute on the left side and simplify both sides of the equation.
3x(x-2) - 1 = x - 0.5(8 + x^2)
3x^2 - 6x - 1 = x - 4 - 0.5x^2
3x^2 - 6x - 1 = x - 4 - 0.5x^2
Next, we will combine like terms and set the equation equal to zero to solve for x.
3x^2 - 6x - 1 = x - 4 - 0.5x^2
3x^2 - 6x - 1 - x + 4 + 0.5x^2 = 0
3x^2 - 6x - x + 4 + 0.5x^2 - 1 = 0
3x^2 - 7x + 3 + 0.5x^2 = 0
3.5x^2 - 7x + 3 = 0
Now, we have a quadratic equation to solve. We can either use the quadratic formula or factorization method to find the values of x. Let's use the quadratic formula:
x = (-(-7) ± √((-7)^2 - 43.53)) / 2*3.5
x = (7 ± √(49 - 42)) / 7
x = (7 ± √7) / 7
x = (7 ± √7) / 7
Therefore, the solutions for the equation are x = (7 + √7) / 7 and x = (7 - √7) / 7.