Solve the equation 9x^2 + 30x + 9 = 0 by completing the square.
The solutions are x₁ = ___ and x₂ = ___ with x₁ ≤ x₂.

Question

Solve the equation 9x^2 + 30x + 9 = 0 by completing the square. The solutions are x₁ = ___ and x₂ = ___ with x₁ ≤ x₂.

SnapAndSolve AI · Accepted Answer

To solve the equation 9x² + 30x + 9 = 0 by completing the square, follow these steps:

Divide the entire equation by 9 to simplify: x² + (30/9)x + 1 = 0, which simplifies to x² + (10/3)x + 1 = 0.
Move the constant term to the other side: x² + (10/3)x = -1.
Complete the square by adding and subtracting (10/6)² = (5/3)² = 25/9 to the left side: x² + (10/3)x + 25/9 = -1 + 25/9.
Rewrite the left side as a square: (x + 5/3)² = -9/9 + 25/9 = 16/9.
Take the square root of both sides: x + 5/3 = ±4/3.
Solve for x: x = -5/3 ± 4/3.
This gives the solutions: x₁ = -3 and x₂ = -1/3.

Therefore, the solutions are x₁ = -3 and x₂ = -1/3 with x₁ ≤ x₂.

Solve the equation 9x^2 + 30x + 9 = 0 by completing the square. The solutions are x₁ = _ and x₂ = _...