Why does the equation 3x2 - 30 = 3 have two solutions but the equation 3x2 + 30 = 3 has no solution?
Try some different values for x.
Let's solve the equation 3x^2 - 30 = 3 first. To find the solutions, we need to isolate x.
Step 1: Add 30 to both sides:
3x^2 - 30 + 30 = 3 + 30
3x^2 = 33
Step 2: Divide both sides by 3:
(3x^2)/3 = 33/3
x^2 = 11
Step 3: Take the square root of both sides to solve for x:
√(x^2) = ±√11
x = ±√11
Therefore, the equation 3x^2 - 30 = 3 has two solutions, x = √11 and x = -√11.
Now, let's solve the equation 3x^2 + 30 = 3. Following the same steps:
Step 1: Subtract 30 from both sides:
3x^2 + 30 - 30 = 3 - 30
3x^2 = -27
Step 2: Divide both sides by 3:
(3x^2)/3 = -27/3
x^2 = -9
Step 3: Take the square root of both sides to solve for x:
√(x^2) = ±√(-9)
x = ±√(-9)
The square root of a negative number is not a real number, so there is no real solution to the equation 3x^2 + 30 = 3.