X-√x+1=5

To solve the equation x-√x+1=5, we can follow these steps:

Step 1: Let's isolate the square root term on one side by subtracting x from both sides: x - x - √x + 1 = 5 - x

Simplifying this gives: -√x + 1 = 5 - x

Step 2: Next, let's isolate the square root term by subtracting 1 from both sides: -√x + 1 - 1 = 5 - x - 1

This simplifies to: -√x = 4 - x

Step 3: Now, let's square both sides of the equation to eliminate the square root: (-√x)^2 = (4 - x)^2

This simplifies to: x = 16 - 8x + x^2

Step 4: Rearrange the equation to form a quadratic equation: x^2 - 9x + 16 = 0

Step 5: Factor or use the quadratic formula to solve the quadratic equation: To factorize the quadratic equation, we need to find two numbers that multiply to give 16 and sum to -9. The numbers that satisfy these criteria are -1 and -16.

So factoring the equation gives us: (x - 1)(x - 16) = 0

Setting each factor equal to zero gives us two possible solutions:

x - 1 = 0, which becomes x = 1 x - 16 = 0, which becomes x = 16

Therefore, the equation x-√x+1=5 has two solutions: x = 1 and x = 16.