Assignment 29
The process of completing the square can be used to solve quadratic equations. Example 1:
The process works even if the solutions are complex numbers. Example 2:
MATH IS POWER.
Problem: Solve by completing the square: x^{2 }- 6x - 13 = 0 Solution (with communication): x^{2 }- 6x - 13 = 0 ==> x^{2 }- 6x = 13 ==> x^{2 }- 6x + 9 = 13 + 9 ==> (x - 3)^{2} = 22 ==> x - 3 = ÷22 or x - 3 = - ÷22 ==> x = 3 + ÷22 or x = 3 - ÷22 ==> x = 7.69 or x = -1.69. Problem: Solve by competing the square: 4x^{2} - 8x - 9 = 0 Solution (with communication): 4x^{2} - 8x - 9 = 0 ==> 4(x^{2 }- 2x) = 9 ==> x^{2} - 2x = 2.25 ==> x^{2} - 2x + 1 = 2.25 + 1 ==> (x - 1)^{2} = 3.25 ==> x - 1 = ÷3.25 or x - 1 = - ÷3.25 ==> x = 1 + ÷3.25 or x = 1 - ÷3.25 ==> x = 2.803 or x = -0.803. |