To find a quadratic equation with solutions of 89 and 29, we can start by recalling that the solutions to a quadratic equation in the form ax^2 + bx + c = 0 are given by the roots of the equation, which are the values of x that satisfy the equation.
Given that the solutions are 89 and 29, we know that the factors of the quadratic equation will be (x - 89) and (x - 29) since these are the expressions that will result in the solutions being 89 and 29, respectively.
To obtain the quadratic equation in standard form (ax^2 + bx + c), we need to multiply the factors (x - 89) and (x - 29) together using FOIL (First, Outer, Inner, Last) method.
1. Start by multiplying the first terms: x * x = x^2
2. Multiply the outer terms: x * (-29) = -29x
3. Multiply the inner terms: (-89) * x = -89x
4. Multiply the last terms: (-89) * (-29) = 2601
Now, combine all the terms:
x^2 - 29x - 89x + 2601
Combine like terms:
x^2 - 118x + 2601
Therefore, the quadratic equation with solutions of 89 and 29 is:
x^2 - 118x + 2601
