Question

Which are the solutions of the quadratic equation?

x2 = 9x + 6
-9 - 105 -9 + 105
2
2
--V57 -9 + V57
2
০ =
(, (
০ ৪ -57৪ + (Sঙ্গ।
O 9 - 105 9 + 105।
2
2

Answer 1

The quadratic equation x² - 9x - 6 = 0 can be solved using the quadratic formula to yield two solutions: x = (9 - √105)/2 and x = (9 + √105)/2.

Step-by-step explanation:

Solving the Quadratic Equation To find the solutions for a quadratic equation of the form ax² + bx + c = 0, we can apply the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). In the case of the equation x² = 9x + 6, we first need to bring all terms to one side of the equation to get it into the standard quadratic form. Hence, we subtract 9x and 6 from both sides to get x² - 9x - 6 = 0.

Applying the quadratic formula, we substitute a = 1, b = -9, and c = -6 into our formula:

• 
  
• x = (9 ± √((9)² - 4(1)(-6))) / (2(1))
• 
  
• x = (9 ± √(81+24)) / 2
• 
  
• x = (9 ± √105) / 2

The solutions of the quadratic equation are therefore x = (9 - √105)/2 and x = (9 + √105)/2.