What method would you choose to solve the equation 2x^2-7=9

1 answer:

3 0

Here is one way to solve for x.

Step 1) 2x^2-7=9

Step 2) 2x^2-7+7=9+7

Step 3) 2x^2=16

Step 4) (2x^2)/2=16/2

Step 5) x^2=8

Step 6) sqrt(x^2)=sqrt(8)

Step 7) |x|=sqrt(8)

Step 8) x=sqrt(8) or x=-sqrt(8)

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Below are explanations/reasons to each of the steps above.

Step 1) Original equation

Step 2) Add 7 to both sides

Step 3) Combine like terms

Step 4) Divide both sides by 2

Step 5) Simplify

Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"

Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x

Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.

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The two solutions are
x = sqrt(8) or x = -sqrt(8)

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Recall the angle sum identity for sine:

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How do i tell if y=x^3+x^2 is even or odd?

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If a function is even, then f(-x) = x.

If a function is odd, then f(-x) = -x.

y = x³ + x² → f(x) = x³ + x² → -f(x) = -(x³ + x²) = -x³ - x²

f(-x) = (-x)³ + (-x)² = [(-1)(x)]³ + [(-1)(x)]² = (-1)³x³ + (-1)²x²

= -1x³ + 1x² =-x³ + x²

f(-x) ≠ f(x) and f(-x) ≠ -f(x)

y = x³ + x² is not odd and not even