To solve this equation, we can try factoring by grouping:
8{x}^{3} - 8{x}^{2} + 1 = 0
First, we can factor out the common factor of 8{x}^{2} from the first two terms:
8{x}^{2}(x - 1) + 1 = 0
Now we have a quadratic expression in terms of (x - 1) that we can factor further:
Let y = x - 1
8{x}^{2}y + 1 = 0
This is in the form of a quadratic equation, and we can solve for y:
8{x}^{2}y = -y = -\frac{1}{8{x}^{2}}
Now, substitute back y = x - 1:
x - 1 = -\frac{1}{8x^2}
Solving for x by cross multiplying:
8x^{3} + 8x^{2} - 1 = 0
This is a cubic equation that can be solved using various methods like factoring, cubic formula, or numerical methods.
To solve this equation, we can try factoring by grouping:
8{x}^{3} - 8{x}^{2} + 1 = 0
First, we can factor out the common factor of 8{x}^{2} from the first two terms:
8{x}^{2}(x - 1) + 1 = 0
Now we have a quadratic expression in terms of (x - 1) that we can factor further:
Let y = x - 1
8{x}^{2}y + 1 = 0
This is in the form of a quadratic equation, and we can solve for y:
8{x}^{2}y = -
y = -\frac{1}{8{x}^{2}}
Now, substitute back y = x - 1:
x - 1 = -\frac{1}{8x^2}
Solving for x by cross multiplying:
8x^{3} + 8x^{2} - 1 = 0
This is a cubic equation that can be solved using various methods like factoring, cubic formula, or numerical methods.