(2-x)2-x(x+1 5)=4

Jasonbradley

2 min read Jun 16, 2024

Solving the Equation: (2-x)^2 - x(x+15) = 4

This article will guide you through the steps to solve the given equation: (2-x)^2 - x(x+15) = 4.

1. Expanding the Equation

The first step is to expand the equation to simplify it:

Expand (2-x)^2: (2-x)^2 = (2-x)(2-x) = 4 - 4x + x^2
Expand x(x+15): x(x+15) = x^2 + 15x

Substituting these expanded terms back into the original equation, we get:

4 - 4x + x^2 - (x^2 + 15x) = 4

2. Simplifying the Equation

Now, let's combine like terms:

Cancel out x^2: The x^2 terms cancel each other out.
Combine x terms: -4x - 15x = -19x

This simplifies the equation to:

4 - 19x = 4

3. Isolate x

To isolate x, we need to move the constant term to the right side of the equation:

Subtract 4 from both sides: 4 - 19x - 4 = 4 - 4
This leaves us with: -19x = 0

4. Solve for x

Finally, divide both sides by -19 to get the value of x:

Divide both sides by -19: -19x / -19 = 0 / -19
Therefore, x = 0

Conclusion

By following these steps, we have successfully solved the equation (2-x)^2 - x(x+15) = 4, finding that x = 0. Remember that the key to solving equations like this is to expand the expressions, simplify them, and then isolate the variable you're trying to solve for.