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How do you solve #2x^2-6=42#?

Answer 1

#x=-2sqrt(6)# or #x=2sqrt(6)#

first move the #6# over #2x^2=48#

then divide by 2 #x^2=24#

now take the square root #x=sqrt(24)#

since x is squared in the equation then x can be negative or positive so we must remember to include this possibility when dealing with powers that are even #x=-2sqrt(6)# or #x=2sqrt(6)#

you should then plug in the numbers and make sure they both work, which they do.

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Answer 2

Julia Adams

To solve the equation (2x^2 - 6 = 42), follow these steps:

Isolate the variable term: Add (6) to both sides of the equation to move the constant term to the other side.

(2x^2 - 6 + 6 = 42 + 6)

(2x^2 = 48)
Divide by the coefficient of the variable term: Since the variable term is (2x^2), divide both sides of the equation by (2).

(\frac{2x^2}{2} = \frac{48}{2})

(x^2 = 24)
Take the square root of both sides: Since (x) is squared, to solve for (x), we take the square root of both sides of the equation.

( \sqrt{x^2} = \pm \sqrt{24} )

(x = \pm \sqrt{24} )
Simplify the square root of 24: ( \sqrt{24} ) can be simplified as ( \sqrt{4 \times 6} = 2\sqrt{6} ).

( x = \pm 2\sqrt{6} )

So, the solutions to the equation (2x^2 - 6 = 42) are (x = 2\sqrt{6}) and (x = -2\sqrt{6}).

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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.