(3-x)(x+4)+x^2=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (3-x)(x+4) + x^2 = 0

This article explores the steps to solve the quadratic equation (3-x)(x+4) + x^2 = 0. We'll break down the solution process, explain the concepts involved, and provide a clear understanding of how to arrive at the final answer.

Expanding the Equation

First, we need to expand the equation by multiplying out the brackets:

(3-x)(x+4) + x^2 = 0

3x + 12 - x^2 - 4x + x^2 = 0

Simplifying the equation, we get:

-x + 12 = 0

Solving for x

Now, we can solve for x:

-x = -12

x = 12

Therefore, the solution to the quadratic equation (3-x)(x+4) + x^2 = 0 is x = 12.

Key Concepts Used

Quadratic Equation: A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Expanding Brackets: Expanding brackets involves multiplying each term inside the first bracket with each term inside the second bracket.
Simplifying: Combining like terms to make the equation easier to solve.
Solving for x: Isolating the variable x to find its value.

Conclusion

By using the principles of expanding brackets, simplifying, and solving for x, we have successfully solved the quadratic equation (3-x)(x+4) + x^2 = 0. The solution to this equation is x = 12.