QuestionAugust 24, 2025

Original Equation: (1)/(6)(-12x^2)+4=-x^2-2 First Step: -2x^2+4=-x^2-2 Answer commutative property of addition associative property of multiplication associative property of addition commutative property of multiplication

Original Equation: (1)/(6)(-12x^2)+4=-x^2-2 First Step: -2x^2+4=-x^2-2 Answer commutative property of addition associative property of multiplication associative property of addition commutative property of multiplication
Original Equation: (1)/(6)(-12x^2)+4=-x^2-2 First Step: -2x^2+4=-x^2-2 Answer commutative property of addition associative property of multiplication associative property of addition commutative property of multiplication

Solution
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Answer

x = \pm \sqrt{6} Explanation 1. Simplify the Left Side Distribute \frac{1}{6} to -12x^2: \frac{1}{6} \times -12x^2 = -2x^2. The equation becomes -2x^2 + 4. 2. Set Equation Equal Equate the simplified left side to the right side: -2x^2 + 4 = -x^2 - 2. 3. Rearrange Terms Move all terms involving x^2 to one side and constant terms to the other: -2x^2 + x^2 = -2 - 4. 4. Combine Like Terms Simplify both sides: -x^2 = -6. 5. Solve for x^2 Divide by -1: x^2 = 6.

Explanation

1. Simplify the Left Side<br /> Distribute $\frac{1}{6}$ to $-12x^2$: $\frac{1}{6} \times -12x^2 = -2x^2$. The equation becomes $-2x^2 + 4$.<br />2. Set Equation Equal<br /> Equate the simplified left side to the right side: $-2x^2 + 4 = -x^2 - 2$.<br />3. Rearrange Terms<br /> Move all terms involving $x^2$ to one side and constant terms to the other: $-2x^2 + x^2 = -2 - 4$.<br />4. Combine Like Terms<br /> Simplify both sides: $-x^2 = -6$.<br />5. Solve for $x^2$<br /> Divide by $-1$: $x^2 = 6$.
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