Consider the following quadratic equation:
x^2−18x+81=0
Step 1 of 2: Using the standard form ax^2+bx+c=0
of the given quadratic equation, factor the left hand side of the equation into two linear factors.
To factor the left hand side of the equation, we can use the quadratic formula or try to find two numbers whose sum is -18 and whose product is 81. In this case, because the coefficient of x^2 is 1, and the constant term is perfect square, it is possible to find the factors by inspection.
The factors of 81 are ±1, ±3, ±9, ±27, ±81. We need to find two numbers whose sum is -18, so we can use -9 and -9.
Therefore, the factored form of the left hand side of the equation is (x - 9)(x - 9).