Which numbers are solutions to the equation h^2 + 4 = 8h - 3? Choose exactly two correct answers. Options: 1, 3, 5, 7.

To find the solutions for the equation h^2 + 4 = 8h - 3, we should first rearrange the equation to bring all terms to one side and set it equal to zero. Here's how we can do it step by step:

1. Subtract '8h' from both sides of the equation to get the terms with 'h' on the same side. 2. Add '3' to both sides to move the constant term to the same side as well. The equation will then be in the standard form of a quadratic equation.

So the steps would look like this:

h^2 + 4 = 8h - 3 h^2 + 4 - 8h + 3 = 0 h^2 - 8h + 7 = 0

Now, we need to factorize the quadratic equation or use another method like completing the square or the quadratic formula to find the solutions. In this case, we can easily factorize:

(h - 7)(h - 1) = 0

Therefore, by setting each factor equal to zero, we get:

h - 7 = 0 or h - 1 = 0 h = 7 or h = 1

The solutions are h = 7 and h = 1. These are the values of h that would satisfy the original equation h^2 + 4 = 8h - 3. So among the options given, 1 and 7 are the correct answers.