(x-2)^3-(x-4)(x^2+4x+16)+6(x+1)^2=49

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-2)^3-(x-4)(x^2+4x+16)+6(x+1)^2=49

This article will guide you through solving the equation (x-2)^3-(x-4)(x^2+4x+16)+6(x+1)^2=49. We will break down the process step-by-step to ensure a clear understanding.

Step 1: Expanding the Equation

Begin by expanding the equation. Remember the following:

• (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
• (a+b)^2 = a^2 + 2ab + b^2
• (a-b)(a^2+ab+b^2) = a^3 - b^3

Applying these formulas, we get:

x^3 - 6x^2 + 12x - 8 - (x^3 - 64) + 6(x^2 + 2x + 1) = 49

Step 2: Simplifying the Equation

Now, simplify the equation by removing the parentheses and combining like terms:

x^3 - 6x^2 + 12x - 8 - x^3 + 64 + 6x^2 + 12x + 6 = 49

This simplifies to:

24x + 62 = 49

Step 3: Solving for x

Isolate the variable 'x' by subtracting 62 from both sides of the equation:

24x = -13

Finally, divide both sides by 24 to find the value of x:

x = -13/24

Therefore, the solution to the equation (x-2)^3-(x-4)(x^2+4x+16)+6(x+1)^2=49 is x = -13/24.