Final answer:
To solve the quadratic equation by completing the square, we arrange it into a perfect square trinomial, add (b/2)^2 to both sides, and take the square root to solve for x, yielding two solutions: x = 7 + √10 and x = 7 - √10.
Step-by-step explanation:
To solve the quadratic equation x²−14x+39=0 by completing the square, we need to rearrange the equation into a form where one side is a perfect square trinomial. Here are the steps to complete the square:
- Start with the original equation: x² - 14x + 39 = 0.
- Move the constant term to the right side: x² - 14x = -39.
- Find the number to complete the square. Divide the coefficient of x by 2, square it, and add to both sides: (-14/2)² = 49. The equation becomes x² - 14x + 49 = -39 + 49.
- Simplify the equation: (x - 7)² = 10.
- Take the square root of both sides: x - 7 = ±√10.
- Solve for x: x = 7 ± √10.
Therefore, the solutions to the equation are x = 7 + √10 and x = 7 - √10.