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Find the root of 9x^2 - 1 -(3x-2)^2 = 0.
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To solve for the root of the quadratic equation 9x^2 - 1 - (3x - 2)^2 = 0, we can use the following steps:
1. Expand the squared term using the identity: (a - b)^2 = a^2 - 2ab + b^2.
9x^2 - 1 - (3x - 2)^2 = 0
9x^2 - 1 - (9x^2 - 12x + 4) = 0
2. Simplify the expression by combining like terms:
9x^2 - 1 - 9x^2 + 12x - 4 = 0
12x - 5 = 0
3. Solve for x by isolating x on one side of the equation by adding 5 to both sides, then dividing by 12:
12x = 5
x = 5/12
Therefore, the root of the given quadratic equation is x = 5/12.
1. Expand the squared term using the identity: (a - b)^2 = a^2 - 2ab + b^2.
9x^2 - 1 - (3x - 2)^2 = 0
9x^2 - 1 - (9x^2 - 12x + 4) = 0
2. Simplify the expression by combining like terms:
9x^2 - 1 - 9x^2 + 12x - 4 = 0
12x - 5 = 0
3. Solve for x by isolating x on one side of the equation by adding 5 to both sides, then dividing by 12:
12x = 5
x = 5/12
Therefore, the root of the given quadratic equation is x = 5/12.