What is x if #-4(x+2)^2+3x=-5#?

Answer 1

#x = -9/4# or # x=-1#

First expand the expression and move the #-5# to the left hand side, to get it into standard form #-4(x^2+4x+4) +3x +5 = 0# #-4x^2 -16x -16 +3x +5 = 0# #-4x^2 -13x -9 = 0# #-(4x^2 +13x+9)=0# #4# and #9# add to give #13#, so the factors we need are #4&1# and #9&1# #-(4x +9)(x+1) = 0# #:. x = -9/4# or # x=-1#
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Answer 2

To find the value of ( x ), we'll first expand and simplify the expression (-4(x+2)^2) and then solve the resulting quadratic equation.

Expanding (-4(x+2)^2), we get: [ -4(x+2)^2 = -4(x^2 + 4x + 4) = -4x^2 - 16x - 16 ]

Substituting this into the equation (-4(x+2)^2 + 3x = -5), we have: [ -4x^2 - 16x - 16 + 3x = -5 ] [ -4x^2 - 13x - 16 + 16 = -5 ] [ -4x^2 - 13x = -5 ]

Rearranging terms, we get the quadratic equation: [ 4x^2 + 13x - 5 = 0 ]

Now, we can use the quadratic formula to solve for ( x ): [ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

Where ( a = 4 ), ( b = 13 ), and ( c = -5 ). [ x = \frac{{-13 \pm \sqrt{{13^2 - 4 \cdot 4 \cdot (-5)}}}}{{2 \cdot 4}} ] [ x = \frac{{-13 \pm \sqrt{{169 + 80}}}}{{8}} ] [ x = \frac{{-13 \pm \sqrt{{249}}}}{{8}} ]

Therefore, the solutions for ( x ) are: [ x = \frac{{-13 + \sqrt{{249}}}}{{8}} ] [ x = \frac{{-13 - \sqrt{{249}}}}{{8}} ]

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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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