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JulsSmile [24]
3 years ago
15

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

Mathematics
1 answer:
alekssr [168]3 years ago
4 0

Answer:

<u>x</u><u> </u><u>is</u><u> </u><u>2</u><u> </u><u>and</u><u> </u><u>-</u><u>8</u>

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

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