Question

Solve x²-8x=3 by completing the square. Which is the solution set of the equation?

O 14-√19, 4+ √/19)
O 14-√11, 4+ √/11}
O 14-√8,4+√8)
O 14-√3,4+√31

Answer 1

To solve the equation x²-8x=3 by completing the square, follow these steps: move the constant term, complete the square on the left side, factor the perfect square trinomial, take the square root, and isolate x. The solution set of the equation is {4 + √19, 4 - √19}.

Step-by-step explanation:

To solve the equation x²-8x=3 by completing the square, follow these steps:

1. Move the constant term (3) to the right side: x²-8x-3 = 0
2. Take half of the coefficient of x (-8), square it, and add it to both sides of the equation. This completes the square on the left side: x²-8x+(-8/2)² = 3 + (-8/2)² → x²-8x+16 = 19
3. Factor the perfect square trinomial: (x-4)² = 19
4. Take the square root of both sides: x-4 = ±√19
5. Add 4 to both sides to isolate x: x = 4 ± √19

Therefore, the solution set of the equation x²-8x=3 is {4 + √19, 4 - √19}. Therefore, the correct option is (14-√19, 4+√19), which matches the set of solutions.

Learn more about Completing the square in quadratic equations