To solve the quadratic equation 2x² – 52 = 49 using the square root property, we first need to rearrange the equation to isolate the x² term.
1. Start by moving 49 to the left side of the equation:
2x² – 52 – 49 = 0
2x² – 101 = 0
2. Next, we add 101 to both sides:
2x² = 101
3. Now, divide both sides by 2 to simplify:
x² = 50.5
4. Now we can apply the square root property, which states that if x² = a, then x = ±√a:
x = ±√50.5
5. To simplify √50.5, we can express it as:
√50.5 = √(101/2) = √101/√2 = (√101)/1.414
We can also leave it as √50.5 for simplicity.
6. Therefore, the two possible values for x are:
x = √50.5 or x = -√50.5
So the solutions to the equation are approximately:
x ≈ 7.1 and x ≈ -7.1.