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What is the solution to the equation below. square root x + 6 = x - 6


What is the solution to the equation below. square root x + 6 = x - 6

alcosby alcosby    3   14.02.2022 07:00    5

Answers
gwendallinesikes gwendallinesikes  14.02.2022 07:00

x = 10

Step-by-step explanation:

\sqrt{x+6} =x-6\\

square both sides:

\implies x+6=(x-6)^2

Expand brackets:

\implies x+6=x^2-12x+36

Collect and combine like terms:

\implies x^2-13x+30=0

\implies (x-10)(x-3)=0

\implies x=10, x=3

Substitute values back into original equation:

x=10: \sqrt{10+6} =10-6 \implies 4 = 4 \ \ \checkmark

x=3: \sqrt{3+6} =3-6 \implies 3 = -3 \ \ \textsf{incorrect!}

Therefore, x=10 only

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