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