Question

Solve the equation by completing the square. x^2-7x-4=0. Have to show steps.

Answer 1

To solve the equation x²-7x-4=0 by completing the square, follow these steps: move the constant term, add the square of half coefficient of x, factor as a perfect square, take the square root, isolate x.

Step-by-step explanation:

To solve the equation by completing the square, follow these steps:

1. Move the constant term to the right side of the equation, so we have x² - 7x = 4.
2. Take half of the coefficient of the x term, square it, and add it to both sides. In this case, half of -7 is -3.5, and when squared, it becomes 12.25. So the equation becomes x² - 7x + 12.25 = 4 + 12.25.
3. Factor the left side of the equation as a perfect square. In this case, it is (x - 3.5)². On the right side, simplify the addition to get x² - 7x + 12.25 = 16.25.
4. Take the square root of both sides to solve for x. So we have x - 3.5 = ±√16.25.
5. Add 3.5 to both sides to isolate x. Thus, the final solutions are x = 3.5 ± √16.25.

Answer 2

x^2-7x-4=0
(x-7/2)^2-(7/2)^2-4=0
(x-7/2)^2-(7)^2/(2)^2-4=0
(x-7/2)^2-49/4-4=0
(x-7/2)^2+(-49-4*4)/4=0
(x-7/2)^2+(-49-16)/4=0
(x-7/2)^2+(-65)/4=0
(x-7/2)^2-65/4=0
(x-7/2)^2-65/4+65/4=0+65/4
(x-7/2)^2=65/4
sqrt[ (x-7/2)^2 ]=+-sqrt(65/4)
x-7/2=+-sqrt(65)/sqrt(4)
x-7/2=+-sqrt(65)/2
x-7/2+7/2=+-sqrt(65)/2+7/2
x=7/2+-sqrt(65)/2
x=[7+-sqrt(65)]/2
x1=[7-sqrt(65)]/2
x2=[7+sqrt(65)]/2