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

Question

Abigail Allen · Accepted Answer

#x = -5/2+-sqrt(33)/2#

The square identity difference can be expressed as follows:

#(a-b)(a+b) = #a^2-b^2

Apply this to #b=sqrt(33)# and #a=(2x+5)#.

To minimize the amount of fraction arithmetic we must perform, first premultiply by #4#.

#0 = 4(x^2 + 5x-2)#

White #color(0) = 4x^2 + 20x-8#

Color(white)(0) = (2x)^2 + 2(2x)(5) + 5^2-33#

#color(white)(0) = sqrt(33))^2-(2x+5)^2#

((2x+5)-sqrt(33))((2x+5)+sqrt(33))#color(white)(0)

#2x+5-sqrt(33))(2x+5+sqrt(33))#color(white)(0)

Thus:

#2x = -5 + -sqrt(33)#

Thus:

#x = (-5/2) + (-sqrt(33)/2#

Hazel Anglin · Answer

undefined To solve the equation x^2 + 5x - 2 = 0 using the completing the square method:

1. Move the constant term to the other side of the equation:
   x^2 + 5x = 2

2. To complete the square, take half of the coefficient of x (which is 5/2) and square it:
   (5/2)^2 = 25/4

3. Add this value to both sides of the equation:
   x^2 + 5x + 25/4 = 2 + 25/4

4. Rewrite the left side as a perfect square trinomial:
   (x + 5/2)^2 = 33/4

5. Take the square root of both sides:
   x + 5/2 = ±√(33/4)

6. Solve for x:
   x = -5/2 ± √(33/4)

Thus, the solutions are x = (-5 ± √33)/2.