the first few steps in solving the quadratic equation 5x2 27x = 14 − 13x by completing the square are shown. 5x2 27x = 14 − 13x
5x2 40x = 14 5(x2 8x) = 14 which is the best step to do next to solve the equation by completing the square? 5(x2 8x 16) = 30 5(x2 8x 16) = 94 5(x2 8x 4) = 18 5(x2 8x 4) = 34
The best step to do next is to add 80 to both sides of equation: 5 ( x² + 8 x ) + 80 = 14 + 80 and since 80 = 5 · 16 5 ( x² + 8 x + 16 ) = 94 Answer : B ) After that we will continue like this: 5 ( x + 4 )² = 94 ( x + 4 )² = 18.8 ... etc
Note that h(x) = 4x^2 - 8x - 60 factors to 4(x^2 - 2x - 15), and that the roots (zeros) of (x^2 - 2x - 15) are -5 and +3. Thus, the smallest zero is -5.
