Answer:
A. 5x + 2x - 4 = 2x2 <- Yes
x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4
B. x^2 - 6x - 7 = 2x <- Yes
x = 4 + sqrt(23) or x = 4 - sqrt(23)
C: 5x^2 – 3x+ 10 = 2x2 <- Yes
x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)
D . 2x^2 – 3x+ 10 = 2x^2 + 21x = -11/3 <- No
Step-by-step explanation:
Solve for x over the real numbers:
5 x + 2 x - 4 = 2 x^2
5 x + 2 x - 4 = 7 x - 4:
7 x - 4 = 2 x^2
Subtract 2 x^2 from both sides:
-2 x^2 + 7 x - 4 = 0
Divide both sides by -2:
x^2 - (7 x)/2 + 2 = 0
Subtract 2 from both sides:
x^2 - (7 x)/2 = -2
Add 49/16 to both sides:
x^2 - (7 x)/2 + 49/16 = 17/16
Write the left hand side as a square:
(x - 7/4)^2 = 17/16
Take the square root of both sides:
x - 7/4 = sqrt(17)/4 or x - 7/4 = -sqrt(17)/4
Add 7/4 to both sides:
x = 7/4 + sqrt(17)/4 or x - 7/4 = -sqrt(17)/4
Add 7/4 to both sides:
Answer: x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4
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Solve for x over the real numbers:
x^2 - 6 x - 7 = 2 x
Subtract 2 x from both sides:
x^2 - 8 x - 7 = 0
Add 7 to both sides:
x^2 - 8 x = 7
Add 16 to both sides:
x^2 - 8 x + 16 = 23
Write the left hand side as a square:
(x - 4)^2 = 23
Take the square root of both sides:
x - 4 = sqrt(23) or x - 4 = -sqrt(23)
Add 4 to both sides:
x = 4 + sqrt(23) or x - 4 = -sqrt(23)
Add 4 to both sides:
Answer: x = 4 + sqrt(23) or x = 4 - sqrt(23)
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Solve for x:
5 x^2 - 3 x + 10 = 2 x^2
Subtract 2 x^2 from both sides:
3 x^2 - 3 x + 10 = 0
Divide both sides by 3:
x^2 - x + 10/3 = 0
Subtract 10/3 from both sides:
x^2 - x = -10/3
Add 1/4 to both sides:
x^2 - x + 1/4 = -37/12
Write the left hand side as a square:
(x - 1/2)^2 = -37/12
Take the square root of both sides:
x - 1/2 = 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)
Add 1/2 to both sides:
x = 1/2 + 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)
Add 1/2 to both sides:
Answer: x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)
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Solve for x over the real numbers:
2 x^2 - 3 x + 10 = 2 x^2 + 21
Subtract 2 x^2 + 21 from both sides:
-3 x - 11 = 0
Multiply both sides by -1:
3 x + 11 = 0
Subtract 11 from both sides:
3 x = -11
Divide both sides by 3:
Answer: x = -11/3
