Question

= (x+1)3 -5x=7+x(x+3)​

Answer 1

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Answer 2

To solve the equation $(x+1)^3 - 5x = 7 + x(x+3)$, you can follow these steps:

1. Expand the left side of the equation by cubing $(x+1)$:

$(x+1)^3 = x^3 + 3x^2 + 3x + 1$

So, the equation becomes:

$x^3 + 3x^2 + 3x + 1 - 5x = 7 + x(x+3)$

2. Simplify the equation by combining like terms:

$x^3 + 3x^2 - 2x + 1 = 7 + x^2 + 3x$

3. Move all the terms to one side of the equation to set it equal to zero:

$x^3 + 3x^2 - 2x + 1 - 7 - x^2 - 3x = 0$

4. Combine like terms again:

$x^3 + 2x^2 - 5x - 6 = 0$

5. Now, you have a cubic equation. Unfortunately, cubic equations do not always have nice analytical solutions like quadratic equations. You may need to use numerical methods or graphing software to approximate the solutions.

If you want to find approximate solutions, you can use numerical methods like the Newton-Raphson method or graph the equation to estimate where it crosses the x-axis.