To solve this equation, we can start by isolating one of the square roots on one side of the equation and then squaring both sides to eliminate the square root.
Let's isolate the square root √(x + 3a) on one side: √(x + 3a) = 7 - √(x - 3)
Now square both sides of the equation to eliminate the square roots: (x + 3a) = (7 - √(x - 3))^2 (x + 3a) = 49 - 14√(x - 3) + (x - 3) (x + 3a) = 49 - 14√(x - 3) + x - 3 x + 3a = 46 - 14√(x - 3)
Now isolate the square root on one side of the equation: 14√(x - 3) = x + 3a - 46 √(x - 3) = (x + 3a - 46)/14
Square both sides again to eliminate the square root: x - 3 = (x + 3a - 46)^2/196 196x - 588 = x^2 + 6ax - 92x - 138a + 2116 196x - 588 = x^2 - 86x - 138a + 2116
This is the simplified form of the equation after completing the square root and squaring steps. The equation is now in standard form, and you can solve it using methods like quadratic formula or factoring to find the values of x that satisfy the equation.
To solve this equation, we can start by isolating one of the square roots on one side of the equation and then squaring both sides to eliminate the square root.
Let's isolate the square root √(x + 3a) on one side:
√(x + 3a) = 7 - √(x - 3)
Now square both sides of the equation to eliminate the square roots:
(x + 3a) = (7 - √(x - 3))^2
(x + 3a) = 49 - 14√(x - 3) + (x - 3)
(x + 3a) = 49 - 14√(x - 3) + x - 3
x + 3a = 46 - 14√(x - 3)
Now isolate the square root on one side of the equation:
14√(x - 3) = x + 3a - 46
√(x - 3) = (x + 3a - 46)/14
Square both sides again to eliminate the square root:
x - 3 = (x + 3a - 46)^2/196
196x - 588 = x^2 + 6ax - 92x - 138a + 2116
196x - 588 = x^2 - 86x - 138a + 2116
Rearrange the equation:
x^2 - 282x + 2704 + 138a - 588 = 0
x^2 - 282x + 2116 + 138a = 0
This is the simplified form of the equation after completing the square root and squaring steps. The equation is now in standard form, and you can solve it using methods like quadratic formula or factoring to find the values of x that satisfy the equation.