To determine the number of solutions, we first need to isolate the square root term on one side of the equation. We can do this by subtracting 5 from both sides of the equation. This will leave us with √x = x - 5. Next, we can square both sides of the equation to eliminate the square root. This will give us x = x^2 - 10x + 25. Finally, we can rearrange the equation to get it in standard quadratic form, which is 0 = x^2 - 11x + 25. We can then use the quadratic formula to solve for x and determine the number of solutions.
Yes, this equation can have more than one solution. Depending on the values of x, the quadratic formula may produce two distinct solutions, one solution, or no real solutions.
If the quadratic formula produces two solutions, it means that the original equation has two distinct solutions. This means that there are two different values of x that satisfy the equation and make it true.
If the discriminant (b^2 - 4ac) in the quadratic formula is negative, it means that the equation has no real solutions. This is because the square root of a negative number is not a real number. In this case, the solutions to the equation would be complex numbers.
Yes, you can use a graph to determine the number of solutions. The number of times the graph of the equation intersects the x-axis is equal to the number of solutions. If the graph intersects the x-axis twice, it means there are two solutions. If the graph intersects the x-axis once, it means there is one solution. And if the graph does not intersect the x-axis at all, it means there are no real solutions to the equation.