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How do you solve #x+3=sqrt(18-2x^2)# algebraically?

Answer 1

Elijah Allen

#{-3}#

Square both sides.

#(x + 3)^2 = (sqrt(18 - 2x^2))^2#

#x^2 + 6x + 9 = 18 - 2x^2#

#3x^2 + 6x - 9 = 0#

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

#x^2 + 2x - 3 = 0#

#(x + 3)(x -1) = 0#

#x = -3 and 1#

Checking in the original equation, you will find that only #x = -3# will work.

Hopefully this helps!

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Answer 2

Serenity Jones

To solve the equation (x + 3 = \sqrt{18 - 2x^2}) algebraically, we can square both sides of the equation to eliminate the square root. This yields a quadratic equation, which can be solved using standard methods such as factoring, completing the square, or using the quadratic formula. After solving for (x), it's important to check the solutions to ensure they are valid within the domain of the original equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.