Lesson 13 Summary
When a quadratic equation is not conducive to factoring, we can solve by completing the square. Completing the square can be used to find solutions that are irrational, something very difficult to do by factoring.
1. The leading coefficient of x2 must be 1
2. Move the constant (c) so that the variables are isolated
3. Take half the (b) coefficient. Square it and add it to both sides
4. Rewrite the equation as perfect square binomial
5. Solve for x
Solve for x:
x2 - 2x = 12
1/2 r2 - 6r = 2
The sum or product of two rational numbers is always a rational number.
The sum of a rational number and an irrational number is always an irrational number.
The product of a rational number and an irrational number is an irrational number as long as the rational number is not zero.
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