How do you solve using completing the square method #x^2+2x-3=0#?

Question

Abigail Allen · Accepted Answer

(x-1)(x+3)

There isn't really a method for this other than figuring out in your head which brackets to multiply to get #x^2+2x-3#. The quadratic formula, #(-b sqrt(b^2-4(a)(c)))/(2a)#, is useful if the numbers don't go into brackets easily. Here, a= #x^2#, b= #2x#, and c= #3#.

Ethan Adkins · Answer

#x=1color(white)("XX")orcolor(white)("XX")x=-3#
#color(white)("XXX")#(see below for "completing the square method" of solution)

Considering #x^2+2x-3=0# Square A squared binomial #(x+a)^2=x^2+2ax+a^2# can be completed. #a=1# (and #a^2=1#) if the first two terms of such a squared binomial are #x^2+2x#. To finish the square, we can add #color(red)(1)#; however, we must subtract #color(red)(1)# once more in order to maintain the equation's accuracy. Color(red)(+1) -3 color(red)(-1)=0#x^2+2x #(x+1)^2 -4=0# #(x+1)^2 = 4# #(x+1) equals +-2# #x=-1+2=1 or #x=-1-2=-3color(white)("XX")or color(white)("XX")

Ethan Adkins · Answer

undefined To solve the equation x^2 + 2x - 3 = 0 using the completing the square method, follow these steps:

1. Move the constant term to the other side of the equation:
   x^2 + 2x = 3

2. Add and subtract the square of half the coefficient of x:
   x^2 + 2x + (2/2)^2 - (2/2)^2 = 3 + (2/2)^2

3. Simplify both sides:
   x^2 + 2x + 1 - 1 = 3 + 1

4. Factor the perfect square trinomial on the left side:
   (x + 1)^2 - 1 = 4

5. Add 1 to both sides to isolate the squared term:
   (x + 1)^2 = 5

6. Take the square root of both sides:
   x + 1 = ±√5

7. Solve for x:
   x = -1 ± √5

Therefore, the solutions to the equation x^2 + 2x - 3 = 0 using the completing the square method are x = -1 + √5 and x = -1 - √5.