Solve the equation for x. if a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
need step by step of how answer was found

The solution of the equation is x = 7 only

Step-by-step explanation:

* Lets solve this equation and then check the answer

∵ √(x - 3) + 5 = x

- At first subtract 5 from both sides

∴ √(x - 3) = x - 5

- To cancel the square root, square the two sides

∵ [√(x - 3)]² = (x - 5)²

- cancel the square root of the left hand side and open the bracket

 power 2 in the right hand side

∴ x - 3 = (x)² + 2(-5)x + (-5)²

∴ x - 3 = x² - 10x + 25

- Add 3 and subtract x from both sides

∴ 0 = x² - 11x + 28

- Its quadratic equation lets factorize it into two brackets

∵ x × x = x²

∵ -4 × -7 = 28

∵ -4x + -7x = -11x

∴ x² - 11x + 28 factorized to (x - 7)(x - 4)

- Equate the two factors by 0

∵ x² - 11x + 28 = 0

∴ (x - 7)(x - 4) = 0

- Let each factor = 0

∴ x - 7 = 0 ⇒ add 7 to both sides

∴ x = 7

OR

x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* Lets check these value of x if both are solution to the given equation

- Substitute the value of x in the given equation

∵ √(x - 3) + 5 = x

- If x = 7

∴ √(7 - 3) + 5 = 7

∴ √4 + 5 = 7

∴ 2 + 5 = 7

∴ 7 = 7

- The left hand side = the right hand side

∴ x = 7 is a solution of the given equation

- If x = 4

∴ √(4 - 3) + 5 = 4

∴ √1 + 5 = 4

∴ 1 + 5 = 4

∴ 6 ≠ 4

- The left hand side ≠ the right hand side

∴ x = 4 is not a solution of the given equation

the ordered pairs for the given function are of the form