How do you solve using the completing the square method #x^2 +5x +4=0#?

Question

Nathan Axel · Accepted Answer

#x=-4" or "x=-1# #"To solve by "color(blue)"completing the square"# add #(1/2"coefficient of the x-term")^2" to both sides"# #"that is " (5/2)^2=25/4# #rArr(x^2+5xcolor(red)(+25/4))+4=0color(red)(+25/4)# #rArr(x+5/2)^2+4=25/4# #rArr(x+5/2)^2=25/4-4=9/4# #color(blue)"take the square root of both sides"# #sqrt((x+5/2)^2)=+-sqrt(9/4)# #rArrx+5/2=+-3/2# #rArrx=-5/2+-3/2# #rArrx_1=-5/2-3/2=-4" and " x_2=-5/2+3/2=-1#

Avery Alexander · Answer

undefined To solve the equation x^2 + 5x + 4 = 0 using the completing the square method, follow these steps:

1. Move the constant term to the other side of the equation: x^2 + 5x = -4.
2. Add the square of half the coefficient of x to both sides of the equation to complete the square: x^2 + 5x + (5/2)^2 = -4 + (5/2)^2.
3. Simplify the equation: x^2 + 5x + 25/4 = 9/4.
4. Rewrite the left side as a squared binomial: (x + 5/2)^2 = 9/4.
5. Take the square root of both sides: x + 5/2 = ±√(9/4).
6. Solve for x: x = -5/2 ± 3/2.

Therefore, the solutions to the equation x^2 + 5x + 4 = 0 are x = -5/2 + 3/2 and x = -5/2 - 3/2, which simplify to x = -1 and x = -4.