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(x-2)^3-x^2(x-6)=4

less than a minute read Jun 17, 2024
(x-2)^3-x^2(x-6)=4

Solving the Equation: (x-2)^3 - x^2(x-6) = 4

This article will walk through the steps to solve the equation (x-2)^3 - x^2(x-6) = 4.

Expanding and Simplifying

  1. Expand the cube: (x-2)^3 = (x-2)(x-2)(x-2) = (x^2 - 4x + 4)(x-2) = x^3 - 6x^2 + 12x - 8

  2. Expand the product: x^2(x-6) = x^3 - 6x^2

  3. Substitute the expansions into the original equation: x^3 - 6x^2 + 12x - 8 - (x^3 - 6x^2) = 4

  4. Simplify by combining like terms: 12x - 8 = 4

Solving for x

  1. Isolate the x term: 12x = 12

  2. Solve for x by dividing both sides by 12: x = 1

Conclusion

Therefore, the solution to the equation (x-2)^3 - x^2(x-6) = 4 is x = 1.

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