Solve 3x^2 -49=0
See your 2:48pm post.
To solve the equation 3x^2 - 49 = 0, we can use the quadratic formula.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 3, b = 0, and c = -49. Plugging these values into the quadratic formula, we get:
x = (-0 ± √(0^2 - 4(3)(-49))) / (2(3))
Simplifying further:
x = (± √(0 + 588)) / 6
x = (± √588) / 6
Now, we simplify the square root of 588:
√588 = √(4 * 147) = √(4 * 3^2 * 7) = 2 * 3√7
Substituting this value back into the equation:
x = (± 2 * 3√7) / 6
We can further simplify this by dividing both the numerator and denominator by 2:
x = (± 3√7) / 3
Finally, we can cancel out the 3's:
x = ± √7
Therefore, the solutions to the equation 3x^2 - 49 = 0 are x = √7 and x = -√7.