Answer:
3. 4x^2+36 =0 only has a complex solution!
Step-by-step explanation:
1. Solve for x over the real numbers:
4 x^2 + 4 x - 36 = 0
Divide both sides by 4:
x^2 + x - 9 = 0
Add 9 to both sides:
x^2 + x = 9
Add 1/4 to both sides:
x^2 + x + 1/4 = 37/4
Write the left hand side as a square:
(x + 1/2)^2 = 37/4
Take the square root of both sides:
x + 1/2 = sqrt(37)/2 or x + 1/2 = -sqrt(37)/2
Subtract 1/2 from both sides:
x = sqrt(37)/2 - 1/2 or x + 1/2 = -sqrt(37)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(37)/2 - 1/2 or x = -1/2 - sqrt(37)/2
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2. Solve for x over the real numbers:
4 x^2 - 4 x - 36 = 0
Divide both sides by 4:
x^2 - x - 9 = 0
Add 9 to both sides:
x^2 - x = 9
Add 1/4 to both sides:
x^2 - x + 1/4 = 37/4
Write the left hand side as a square:
(x - 1/2)^2 = 37/4
Take the square root of both sides:
x - 1/2 = sqrt(37)/2 or x - 1/2 = -sqrt(37)/2
Add 1/2 to both sides:
x = 1/2 + sqrt(37)/2 or x - 1/2 = -sqrt(37)/2
Add 1/2 to both sides:
Answer: x = 1/2 + sqrt(37)/2 or x = 1/2 - sqrt(37)/2
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3. Solve for x:
4 (x^2 + 9) = 0
Divide both sides by 4:
x^2 + 9 = 0
Subtract 9 from both sides:
x^2 = -9
Take the square root of both sides:
Answer: x = 3 i or x = -3 i
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4. Solve for x over the real numbers:
4 x^2 - 36 = 0
Add 36 to both sides:
4 x^2 = 36
Divide both sides by 4:
x^2 = 9
Take the square root of both sides:
Answer: x = 3 or x = -3
