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haileesprague3999
28.06.2019 •
Mathematics
Solve 2x2 + 5x = 12. a. x= three over two and x = −4 b. x = 2 and x = −3 c. x = −6 and x = 5 d. x = one over two and x = one over three
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Ответ:
A. x= three over two and x = −4
Step-by-step explanation:
2x^2 + 5x = 12
I will use complete the square
Divide each side by 2
2x^2 /2 + 5/2 x = 12/2
x^2 +5/2 x =6
Take 5/2 , divide by 2 and then square it
5/2 ÷2 = 5/2 (5/4) ^2 = 25/16
Add this to both sides
x^2 + 5/2 x + 25/16 = 6 + 25/16
(x+5/4)^2 = 6 *16/16 + 25/16
(x+5/4)^2 = 96/16 +25/16
(x+5/4)^2 = 121/16
Take the square root of each side
sqrt((x+5/4)^2) = sqrt(121/16)
x+5/4 = ±11/4
Subtract 5/4 from each side
x+5/4-5/4 = ±11/4 -5/4
x = ±11/4 -5/4
x = -11/4 - 5/4 and x = 11/4 - 5/4
x = -16/4 = -4 and x = 6/4 = 3/2
Ответ: