Question

solve quadractic equation x2-12x+32=0 using formulamethod​

Answer 1

This has roots given by the quadratic formula:

$x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac } }{2a} \\ = \frac{12</p><p>± \sqrt{12 {}^{2} - 4 \times 1 \times 32} }{2 \times 1} \\ </p><p>= \frac{1± \sqrt{144 - 128} }{2} \\ </p><p>= \frac{12± \sqrt{16} }{2} \\ </p><p> = \frac{12±4}{2} \\ </p><p> = 6±2$

So x=8 or x=4

Answer 2

Question:

solve quadractic equation x2-12x+32=0 using formula method

Solution:

$x = 4 \: \: \: \: (or) \: \: \: x = \: 8$

Explanation:

Method 1 - Finding a pair of factors

Find a pair of factors of 32 with sum 12

The pair 4,8 works in that 4x8=32 and 4+8=12

Hence we find:

$0={x}^{2}-12x+32=(x-4)(x-8)$

$So \: \: x = 4 \: \: or \: \: x = 8$

(Or)

Method 2 - Completing the square

$0 = {x}^{2} - 12x + 32$

$\: \: \: \:= {x}^{2} - 2(6x) + 36 - 4$

$\: \: \: \: = (x - {6)}^{2} - {2}^{2}$

$\: \: \: \: = ((x - 6) - 2)((x - 6) + 2)$

$x = (x - 8)(x - 4)$

$Hence \: x = 8 \: (or) \: x = 4$