To solve the equation √x – 5 = 7 – 11, we first simplify the right side of the equation. Since 7 – 11 equals -4, we can rewrite the equation as:
√x – 5 = -4
Next, we isolate the square root by adding 5 to both sides:
√x = -4 + 5
This simplifies to:
√x = 1
Now, to get rid of the square root, we square both sides:
(√x)² = 1²
This results in:
x = 1
Finally, we can verify the solution by substituting x back into the original equation:
√1 – 5 = 7 – 11
0 = -4
Since we have a contradiction, it indicates that there is no solution for the value of x that satisfies the original equation. Therefore, the equation has no real solutions.