Question

12. Solve x^2 + 6x - 16 = 0 by completing the square. Please help and show work

Answer 1

Answer:

x is 2 and -8

Step-by-step explanation:

${x}^{2} + 6x - 16 = 0$

general equation

${ax}^{2} + (sum)x + product = 0$

sum is 6, product is -16

for completing squares,

first divide the sum by 2:

$= \frac{6}{2} = 3$

add the square of the result on (x² + 6x) and subtract it from the product:

$( {x}^{2} + 6x + {3}^{2} ) - 16 - {3}^{2} = 0 \\ {(x + 3)}^{2} - 25 = 0 \\ {(x + 3)}^{2} = 25$

take square root:

$\sqrt{ {(x + 3)}^{2} } = \sqrt{25 } \\ x + 3 = ±5 \\ x = ±5 - 3$

x is either: 5-3 or -5-3

$x = 2 \: \: and \: - 8$