How do you solve #x^2-30=0# using the quadratic formula?

Answer 1

We must convert our quadratic into standard form in order to use the quadratic formula:

#ax^2+bx+c=0#

We already have our quadratic in this format:

#x^2-30= 1x^2 + 0x -30 =0#

Therefore

#a=1," " b=0 " & " c=-30#

Next, we apply the formula for quadratics:

#x_(+-) = (-b+-sqrt(b^2-4ac))/(2a)#
#x_(+-) = (0+-sqrt(0-4*1*(-30)))/(2*1)#
#x_(+-) = +-sqrt(120)/(2)#
we can bring the #2# from the denominator up into the square root by first squaring it
#x_(+-) = +-sqrt(120/4)=+-sqrt(30)#
Which is the answer that we would have arrived at by just moving the #-30# to the right hand side and taking the square root of both sides.
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Answer 2

To solve the equation (x^2 - 30 = 0) using the quadratic formula, follow these steps:

  1. Identify the coefficients (a), (b), and (c) in the equation (ax^2 + bx + c = 0). In this case, (a = 1), (b = 0), and (c = -30).
  2. Substitute the values of (a), (b), and (c) into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
  3. Plug in the values: (x = \frac{{-0 \pm \sqrt{{0^2 - 4 \cdot 1 \cdot (-30)}}}}{{2 \cdot 1}}).
  4. Simplify under the square root: (x = \frac{{\pm \sqrt{{0 + 120}}}}{2}).
  5. Further simplify: (x = \frac{{\pm \sqrt{{120}}}}{2}).
  6. Simplify the square root: (x = \frac{{\pm \sqrt{{4 \cdot 30}}}}{2}).
  7. Extract the perfect square: (x = \frac{{\pm 2\sqrt{{30}}}}{2}).
  8. Simplify: (x = \pm \sqrt{{30}}).

So, the solutions to the equation (x^2 - 30 = 0) are (x = \sqrt{30}) and (x = -\sqrt{30}).

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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.

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.

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.

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.

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