2%2B(x%2B1)2%3D6x%2B47.jpeg "(2x+1)2+(x+1)2=6x+47")
Solving the Quadratic Equation: (2x+1)2 + (x+1)2 = 6x + 47
This article will guide you through the process of solving the quadratic equation (2x+1)2 + (x+1)2 = 6x + 47.
1. Expanding the Equation
First, we need to expand the squares on the left side of the equation:
(2x+1)2 + (x+1)2 = 6x + 47 (4x2 + 4x + 1) + (x2 + 2x + 1) = 6x + 47
2. Simplifying the Equation
Combine like terms on the left side:
5x2 + 6x + 2 = 6x + 47
3. Rearranging the Equation
Subtract 6x and 47 from both sides to get a standard quadratic equation:
5x2 - 45 = 0
4. Solving for x
Now, we can solve for x using the quadratic formula:
x = (-b ± √(b2 - 4ac)) / 2a
Where:
- a = 5
- b = 0
- c = -45
Plugging in the values:
x = (0 ± √(02 - 4 * 5 * -45)) / 2 * 5 x = ± √(900) / 10 x = ± 30 / 10
Therefore, the solutions to the equation are:
- x = 3
- x = -3
Conclusion
By expanding, simplifying, rearranging, and applying the quadratic formula, we successfully solved the equation (2x+1)2 + (x+1)2 = 6x + 47 and found the solutions x = 3 and x = -3.