When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

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Let the positive number be represented by the variable x.

Translate the problem into an equation: The square of the number is x², twice the number is 2x, and the sum of 6 and twice the number is 6 + 2x. Subtracting this from the square of the number gives the equation x² - (6 + 2x) = 0.

Simplify the equation by distributing the negative sign: x² - 6 - 2x = 0.

Rearrange the equation into standard quadratic form: x² - 2x - 6 = 0.

Solve the quadratic equation x² - 2x - 6 = 0 using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -2, and c = -6. Simplify the discriminant and solve for x, ensuring to only consider the positive solution since the problem specifies a positive number.

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