How do you solve #x(x-4)-2=43#?

Answer 1
I would start by multiplying the #x# to get rid of the bracket: #x^2-4x-2=43# rearranging: #x^2-4x-2-43=0# #x^2-4x-45=0# so that: #x_(1,2)=(4+-sqrt(16-4(1*-45)))/2=(4+-sqrt(196))/2=(4+-14)/2# So, you get two solutions: #x_1=18/2=9# #x_2=-10/2=-5#

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Answer 2

To solve the equation (x(x-4)-2=43):

  1. Expand and simplify the left side of the equation: (x(x-4)-2 = x^2 - 4x - 2)

  2. Set the equation equal to 43: (x^2 - 4x - 2 = 43)

  3. Subtract 43 from both sides to set the equation to zero: (x^2 - 4x - 2 - 43 = 0) (x^2 - 4x - 45 = 0)

  4. Now, we have a quadratic equation in the form (ax^2 + bx + c = 0), where (a = 1), (b = -4), and (c = -45).

  5. To solve for (x), you can use the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}})

  6. Substitute the values: (x = \frac{{-(-4) \pm \sqrt{{(-4)^2 - 4 \cdot 1 \cdot (-45)}}}}{{2 \cdot 1}})

  7. Simplify under the square root: (x = \frac{{4 \pm \sqrt{{16 + 180}}}}{2}) (x = \frac{{4 \pm \sqrt{{196}}}}{2})

  8. Simplify the square root: (x = \frac{{4 \pm 14}}{2})

  9. Simplify further: (x_1 = \frac{{4 + 14}}{2} = \frac{{18}}{2} = 9) (x_2 = \frac{{4 - 14}}{2} = \frac{{-10}}{2} = -5)

So, the solutions to the equation (x(x-4)-2=43) are (x = 9) and (x = -5).

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Answer 3

To solve the equation x(x-4)-2=43, follow these steps:

  1. Expand the expression x(x-4) to get x^2 - 4x.
  2. Rewrite the equation as x^2 - 4x - 2 = 43.
  3. Move 43 to the left side of the equation by subtracting 43 from both sides: x^2 - 4x - 2 - 43 = 0.
  4. Combine like terms: x^2 - 4x - 45 = 0.
  5. Factor the quadratic equation: (x - 9)(x + 5) = 0.
  6. Set each factor equal to zero and solve for x:
    • Set x - 9 = 0 and solve for x: x = 9.
    • Set x + 5 = 0 and solve for x: x = -5.

Therefore, the solutions to the equation are x = 9 and x = -5.

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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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