Solve the equation by completing the square: 2x^2 - 7x = -12
A. x = 7-i√47/4, x = 7+i√47/4
B. x = 6, x = 1
C. x ≈ 4.8, x ≈ -1.3
D. x = 7-i√145/4, x = 7+i√145/4
Algebra 2 help please?
2016-02-11 2:00 pm
回答 (3)
2016-02-11 2:26 pm
2x² − 7x = −12
divide both sides by 2 and get
x² − (7/2)x = −6
x² −2(7/4)x = −6
Add (7/4)² to both sides and get
x² −2(7/4)x + (7/4)² = −6+ (7/4)²
{x - (7/4)}² = −6+ 49/16
{[x - (7/4)}² = −47/16
x − (7/4) = √( −47/16)
x - (7/4) =± i(√47)/4
x = (7/4) ± i(√47)/4
i.e. x = (7 + i√47)/4 or x = (7 − i√47)/4
Hence A
divide both sides by 2 and get
x² − (7/2)x = −6
x² −2(7/4)x = −6
Add (7/4)² to both sides and get
x² −2(7/4)x + (7/4)² = −6+ (7/4)²
{x - (7/4)}² = −6+ 49/16
{[x - (7/4)}² = −47/16
x − (7/4) = √( −47/16)
x - (7/4) =± i(√47)/4
x = (7/4) ± i(√47)/4
i.e. x = (7 + i√47)/4 or x = (7 − i√47)/4
Hence A
2016-02-11 2:09 pm
2x² - 7x = -12
2[x² - (7/2)x] = -12
x² - (7/2)x = -6
x² - 2(7/4)x + (7/4)² = -6 + (7/4)²
[x - (7/4)]² = (-96/16) + (49/16)
[x - (7/4)]² = -47/16
x - (7/4) = √(-47/16)
x - (7/4) = i(√47)/4 or x - (7/4) = -i(√47)/4
x = (7/4) + i(√47)/4 or x = (7/4) - i(√47)/4
x = (7 + i√47)/4 or x = (7 - i√47)/4
..... The answer is (A).
2[x² - (7/2)x] = -12
x² - (7/2)x = -6
x² - 2(7/4)x + (7/4)² = -6 + (7/4)²
[x - (7/4)]² = (-96/16) + (49/16)
[x - (7/4)]² = -47/16
x - (7/4) = √(-47/16)
x - (7/4) = i(√47)/4 or x - (7/4) = -i(√47)/4
x = (7/4) + i(√47)/4 or x = (7/4) - i(√47)/4
x = (7 + i√47)/4 or x = (7 - i√47)/4
..... The answer is (A).
2016-02-11 4:08 pm
2x^2 - 7x = -12
x^2 - (7/2)x + 6 = 0
(x - 7/4)^2 + 47/16 = 0
Answer choice:
A. x = 7 - i√47/4, x = 7 + i√47/4
x^2 - (7/2)x + 6 = 0
(x - 7/4)^2 + 47/16 = 0
Answer choice:
A. x = 7 - i√47/4, x = 7 + i√47/4
收錄日期: 2021-04-20 16:17:19
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