Rewriting the equation as a proportion, we have (1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10)/4x (2x/4x) + (2/4x) = (x^2 - 7x + 10)/4x
Multiplying both sides of the equation by 4x to clear the denominators: 2x + 2 = x^2 - 7x + 10 We now have a new equation that is equivalent to the original equation: x^2 - 9x + 8 = 0
We can also write the equation into its factored form: (x - 8)(x - 1) = 0 Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero. x - 8 = 0 => x = 8 x - 1 = 0 => x = 1 Therefore, our solutions are x = 8 and x = 1.
