9514 1404 393
Answer:
x = ±6
Step-by-step explanation:
-x^2 = -36 . . . . . . given
x^2 = 36 . . . . . . . multiply by -1 to undo the multiplication by -1*
x = ±√36 = ±6 . . . square root to undo the square
The solution is x = -6 or +6.
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Additional comments
* We could have erased the minus signs by adding (x²+36) to both sides of the equation. This would treat each negative term as the result of a subtraction, rather than the result of a multiplication (or division) by -1.
If we consider the minus signs to be the result of multiplication by -1, then the "undo" (inverse) operation is multiplication by the reciprocal of -1: 1/-1 = -1. That is what we show above.
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An algebraic solution always involves inverse operations. Algebra is all about using inverse operations to solve equations. Graphical or iterative solutions, not so much.
