0.5x^2-2x+2=0

3 min read Jun 10, 2024
0.5x^2-2x+2=0

Tentu, ini artikel tentang persamaan kuadrat $0.5x^2 - 2x + 2 = 0$:

Solving the Quadratic Equation: 0.5x^2 - 2x + 2 = 0

This equation is a quadratic equation in the standard form: ax^2 + bx + c = 0, where a = 0.5, b = -2, and c = 2.

Here are the common methods to solve quadratic equations:

1. Factoring

  • Identify factors: In this case, the equation cannot be easily factored into two binomials with integer coefficients.

2. Completing the Square

  • Isolate the x^2 and x terms: 0.5x^2 - 2x = -2
  • Divide both sides by the coefficient of x^2 (0.5): x^2 - 4x = -4
  • Complete the square on the left side: Take half of the coefficient of the x term (-4), square it (4), and add it to both sides. x^2 - 4x + 4 = -4 + 4
  • Factor the left side as a perfect square trinomial: (x - 2)^2 = 0
  • Solve for x: x - 2 = 0 x = 2

Therefore, the solution to the equation is x = 2.

3. Quadratic Formula

  • Apply the formula: The quadratic formula provides a direct solution for any quadratic equation. x = (-b ± √(b^2 - 4ac)) / 2a
  • Substitute the values: x = (2 ± √((-2)^2 - 4 * 0.5 * 2)) / (2 * 0.5) x = (2 ± √(4 - 4)) / 1 x = (2 ± √0) / 1 x = 2

Therefore, the solution to the equation is x = 2.

Conclusion

Using different methods, we find that the equation 0.5x^2 - 2x + 2 = 0 has a single solution, x = 2. This means the parabola represented by the equation intersects the x-axis at only one point.

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