1.Use factoring to solve the quadratic equation.

x2 - 64 = 63x

Rearrange with zero on one side and note that 64 - 1 = 63. That will give you a clue to the factoring

To solve the quadratic equation x^2 - 64 = 63x using factoring, we need to rewrite it in the standard form:

x^2 - 63x - 64 = 0

Now, let's try to factor the equation by looking for two numbers whose product is -64 and whose sum is -63x. We can break down -64 into its factors:

-64 can be written as (-8) * 8 or (8) * (-8)
-64 can be written as (-1) * 64 or (1) * (-64)

Next, we need to find the pair of factors that add up to -63x. In this case, none of the above factor pairs satisfy this condition.

Since we cannot factor the equation directly, we can resort to another method called the quadratic formula to find the solutions. The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, the coefficients are: a = 1, b = -63, and c = -64. Let's substitute these values into the quadratic formula:

x = (63 ± √((-63)^2 - 4 * 1 * (-64))) / (2 * 1)

Simplifying further:

x = (63 ± √(3969 + 256)) / 2
x = (63 ± √4225) / 2

Now, we have two possibilities for x:

1. x = (63 + √4225) / 2
2. x = (63 - √4225) / 2

Calculating the square root:

1. x = (63 + 65) / 2 = 128 / 2 = 64
2. x = (63 - 65) / 2 = -2 / 2 = -1

Hence, the solutions to the quadratic equation x^2 - 64 = 63x are x = 64 and x = -1.