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How do you solve #-2(x+3)^2 + 7 = -25#?

Answer 1

#x =-1 " or " x=-7#

The usual approach with a quadratic equation is to make it equal to 0. However, this one is a special case - there is no #x# term.

First isolate the bracket:

#-2(x+3)^2 color(red)(+7) =-25#

#-2(x+3)^2 =-25 color(red)(-7)#

#color(blue)(-2)(x+3)^2 =-32#

#(x+3)^2 = (-32)/(color(blue)(-2)) = 16#

#x+3 = +-sqrt16#

#x = +4-3 = 1#

#x =-4-3 =-7#

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Answer 2

Avery Alexander

To solve the equation -2(x+3)^2 + 7 = -25, you can follow these steps:

Subtract 7 from both sides of the equation: -2(x+3)^2 = -25 - 7 = -32.
Divide both sides by -2: (x+3)^2 = -32 / -2 = 16.
Take the square root of both sides: √(x+3)^2 = √16.
Solve for x+3: x+3 = ±4.
Subtract 3 from both sides: x = -3 ± 4.
Solve for both possible values of x:
- For x = -3 + 4, x = 1.
- For x = -3 - 4, x = -7.
Therefore, the solutions to the equation -2(x+3)^2 + 7 = -25 are x = 1 and x = -7.

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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.