Solve x=(x+6)^1/2

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve for x given that x=(x+6)^1/2

x = (x+6)^1/2

square both the sides

=> x^2 = x + 6

=> x^2 - x - 6 = 0

=> x^2 - 3x + 2x - 6 =0

=> x (x - 3) + 2(x - 3) = 0

=> (x + 2)(x - 3) = 0

From x + 2 = 0 , we get x = -2

From x - 3 = 9, we get x = 3

We eliminate the negative root.

Therefore x is equal to 3.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll eliminate the square root from the right side. For this reason, we'll square both sides.

x^2 = [(x+6)^1/2]^2

x^2 = x + 6

We'll subtract x + 6 both sides:

x^2 - x - 6 = 0

We'll factorize and we'll get:

(x - 3)(x + 2) = 0

x - 3 = 0

x = 3

x + 2 = 0

x = -2

We'll verify the values of x in the equation:

x = 3

3 = sqrt(3+6)

3 = sqrt9

3 = 3

x = -2

-2 =  sqrt(-2+6)

-2 = sqrt4

-2 is different from 2.

So, we'll reject the solution x = -2.

The only solutionof the equation is x = 3.

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