To solve the first equation 2x^(2) + 14 = 0:
Subtract 14 from both sides:2x^(2) = -14
Divide by 2:x^(2) = -7
Take the square root of both sides (remember to consider both the positive and negative square root):x = ±√(-7)
Therefore, the solutions for 2x^(2) + 14 = 0 are:x = √(-7) or x = -√(-7)
To solve the second equation 4x^(2) - x = 0:
Factor out x:x(4x - 1) = 0
Set each factor to zero:x = 0 or 4x - 1 = 0
For 4x - 1 = 04x = 1x = 1/4
Therefore, the solutions for 4x^(2) - x = 0 are:x = 0 or x = 1/4
To solve the first equation 2x^(2) + 14 = 0:
Subtract 14 from both sides:
2x^(2) = -14
Divide by 2:
x^(2) = -7
Take the square root of both sides (remember to consider both the positive and negative square root):
x = ±√(-7)
Therefore, the solutions for 2x^(2) + 14 = 0 are:
x = √(-7) or x = -√(-7)
To solve the second equation 4x^(2) - x = 0:
Factor out x:
x(4x - 1) = 0
Set each factor to zero:
x = 0 or 4x - 1 = 0
For 4x - 1 = 0
4x = 1
x = 1/4
Therefore, the solutions for 4x^(2) - x = 0 are:
x = 0 or x = 1/4