%2B1-2x-2-7%3D0.jpeg "0 3x(x-4)+1 2x-2 7=0")
Solving the Quadratic Equation: 3x(x-4) + 12x - 27 = 0
This article will guide you through the steps of solving the quadratic equation 3x(x-4) + 12x - 27 = 0.
1. Expanding the Equation:
First, we need to simplify the equation by expanding the product:
3x(x-4) + 12x - 27 = 0 3x² - 12x + 12x - 27 = 0 3x² - 27 = 0
2. Isolating the x² term:
Next, we isolate the x² term by adding 27 to both sides of the equation:
3x² - 27 + 27 = 0 + 27 3x² = 27
3. Solving for x²:
Now, we solve for x² by dividing both sides by 3:
3x²/3 = 27/3 x² = 9
4. Taking the Square Root:
To find the value of x, we take the square root of both sides of the equation:
√(x²) = ±√9 x = ±3
5. Final Solution:
Therefore, the solutions to the quadratic equation 3x(x-4) + 12x - 27 = 0 are x = 3 and x = -3.
Conclusion
We have successfully solved the quadratic equation by expanding, simplifying, and isolating the x² term. This process demonstrates the importance of applying algebraic techniques to find the roots of polynomial equations.