Solve:
sq root of (x+1) minus 3 = sq root of
(x+4)
when I solve it I get zero, but when I plug it back in only one answer works. do both have to work for it to have a solution?
To solve the equation √(x+1) - 3 = √(x+4), you can follow these steps:
1. Start by isolating one of the square roots. Add 3 to both sides of the equation to get √(x+1) = √(x+4) + 3.
2. Square both sides of the equation to eliminate the square root. This gives you (x+1) = (x+4) + 6√(x+4) + 9.
3. Simplify the equation by combining like terms. Move all terms to one side to get (x+1) - (x+4) - 9 = 6√(x+4).
4. Further simplify the equation to get -3 - 9 = 6√(x+4).
5. Simplify the left side of the equation to -12 and square both sides to eliminate the square root. This gives you (-12)^2 = (6√(x+4))^2.
6. Simplify the equation to get 144 = 36(x+4).
7. Expand and solve for x. This results in 144 = 36x + 144.
8. Subtract 144 from both sides to get 0 = 36x.
9. Divide both sides by 36 to solve for x and obtain x = 0.
Now, we need to check if this solution works by plugging it back into the original equation.
For x = 0, the original equation becomes √(0+1) - 3 = √(0+4), which simplifies to √1 - 3 = √4.
The left side becomes 1 - 3 = 2, which is not equal to the right side, 2.
So, even though x = 0 is a solution to the equation, it does not satisfy the original equation.
Therefore, the equation has no solution, and x = 0 does not work as a valid solution.