Hi I do not how to simplify the problem

x^2 =40+12sqrt2

what would be x? BTW if you sqrt both sides it would be double square root so what then? how to simplify?

12 sqrt 2 = x^2 - 40

144 (2) = x^4 -80 x^2 + 1600
x^4 - 80 x^2 + 1312 = 0
graph to find zeros
http://mathportal.org/calculators/polynomials-solvers/polynomial-graphing-calculator.php

zeros at
x = -7.55, -4.80 + 4.80, +7.55
check those in original
+ and - 7.55 works
the 4.8 does not

To simplify the equation x^2 = 40 + 12√2 and find the value of x, follow these steps:

1. Start by subtracting 40 from both sides of the equation. This gives you x^2 - 40 = 12√2.
2. Next, divide both sides of the equation by 12 to isolate the square root term. This will result in (x^2 - 40)/12 = √2.
3. Now, you can square both sides of the equation to eliminate the square root term. However, you are correct that squaring both sides will result in a double square root. But don't worry, we will handle that.
- On the left side of the equation, since it is already x^2, it remains the same: (x^2 - 40)^2/12^2 = (√2)^2.
- Simplifying the equation gives you (x^2 - 40)^2/144 = 2.
4. To further simplify, cross-multiply to get (x^2 - 40)^2 = 288.
5. Take the square root of both sides to eliminate the exponent of 2. This gives you √(x^2 - 40)^2 = √288.
- At this point, it's important to note that the square root can have two values: positive and negative.
6. Simplifying the equation, you get x^2 - 40 = ±√288.
7. Add 40 to both sides of the equation to isolate x^2. The equation becomes x^2 = 40 ± √288.
8. Finally, take the square root of both sides to solve for x. Remember to consider both the positive and negative square roots: x = ±√(40 ± √288).

Now, you have both the positive and negative values of x that satisfy the equation x^2 = 40 + 12√2.