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3 years ago

What is equivalent to 0 = 2x2 - 16x – 18 when completing the square?

Mathematics

1 answer:

algol133 years ago

6 0

Answer:

x = 1

x = -9

Step-by-step explanation:

(2x2 + 16x) - 18 = 0

2x2 + 16x - 18 = 2 • (x2 + 8x - 9)

x2 + 8x - 9

-9 + 1 = -8

-3 + 3 = 0

-1 + 9 = 8

2 • (x + 9) • (x - 1) = 0

2 = 0

x+9 = 0

x = -9

x-1 = 0

x = 1

x2 + 8x - 9 = 0

x2+8x = 9

(x+4) • (x+4) =

(x+4)2

x2+8x+16 = 25 and

x2+8x+16 = (x+4)2

(x+4)2 = 25

x = -4 + √ 25

x2 + 8x - 9 = 0

has two solutions:

x = -4 + √ 25

x = -4 - √ 25

- B ± √ B2-4AC

x = ————————

A = 1

B = 8

C = -9

B2 - 4AC =

64 - (-36) =

100

-8 ± √ 100

x = —————

x = ( -8 ± 10) / 2

x =(-8+√100)/2=-4+5= 1.000

or:

x =(-8-√100)/2=-4-5= -9.000

Answer: x = 1

x = -9

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