Step-by-step explanation: When an equation has a squared term in it
such as x² - 2x - 63 = 0, it's called a polynomial equation.
The rule for solving a polynomial equation is
to first set it equal to 0, them factor.
Since this equation is already set equal to 0, we can factor the left side.
To factor x² - 2x - 63, look for factors of -63 that add to -2.
In this case, these factors are -9 and +7.
So we have (x - 9)(x + 7) = 0.
When two terms are multiplying together to equal 0,
either one term or the other must equal 0.
So x - 9 = 0 or x + 7 = 0.
Solving for x in each equation, we get x = 9 or x = -7.
So this equation has two solutions and we write out answer
in set notation which looks like this {9, -7}.
