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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.