Solve the equation by completing the square. (1 point) Responses 10.35, 1.35 10.35, 1.35 10.35, 10.35, Image with alt text: negative 1 point 35 Image with alt text: negative 10.35, negative 1.35 , 1.35 Image with alt text: negative 10.35 , 1.35
To solve the equation by completing the square, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.
Let's say our equation is x^2 - 2x - 3 = 0.
1. Move the constant term to the right side of the equation: x^2 - 2x = 3
2. Take half of the coefficient of the x-term, square it, and add it to both sides of the equation:
x^2 - 2x + (-2/2)^2 = 3 + (-2/2)^2
x^2 - 2x + 1 = 3 + 1
x^2 - 2x + 1 = 4
3. Factor the left side of the equation: (x - 1)^2 = 4
4. Take the square root of both sides: x - 1 = ±sqrt(4)
5. Solve for x:
x - 1 = 2 or x - 1 = -2
x = 2 + 1 or x = -2 + 1
x = 3 or x = -1
Therefore, the solutions to the equation x^2 - 2x - 3 = 0 are x = 3 and x = -1.