how do I complete the square for 2x^2+9x+4=0

Question

cydney_morgan · Answer

The expression you have given is not an equation (does not equal something), so it cannot be solved.  I am going to assume that the expression is supposed to equal zero, and then solve that equation.

The equationthat I am going to solve is 2x2 - 9x + 4 = 0.  The method I am going to use is called completing the square.

2x2 - 9x + 4 = 0

2x2 - 9x + 4 -4 = 0 -4              Subtract 4 from each side

2x2 - 9x = -4                               Simplify

(2x2 - 9x)/x = -4/2                      Divide both sides by two (the coefficient of x2)

x2 -9/2*x = -2                            Distribute on the left, simplify the right

x2 - 9/2*x + 81/16 = -2 + 81/16   Add 81/16 to each side (divide the coefficient on x by two, then square 

                                                  the result)

(x - 9/4)2 = -2 + 81/16                  Factor the left side as a perfect square (9/4 is the square root of 

                                                  81/16)

(x - 9/4)2 = -32/16 + 81/16           Change the fractions on the right so that they have common

                                                  denominators

(x - 9/4)2 = 49/16                        Simplify

x - 9/4 = +/- sqrt(49/16)              Take the square root of both sides (sqrt means square root)

x - 9/4 = +/- 7/4                         Simplify

x - 9/4 = 7/4 or x -9/4 = -7/4       Separate the problem into positive and negative values on the right

x - 9/4 + 9/4 = 7/4 +9/4 or          Add 9/4 to both sides on both possible solutions

x - 9/4 + 9/4 = -7/4 + 9/4

x = 16/4 or x = 2/4                     Simplify each solution

x = 4 or x = 1/2                          Reduce the fractions

Completing the square is a valuable tool to use, because any binomial equation can be solved with it.  Even though you could find the answer to this problem without it, I wanted to give you a chance to learn how to use it.

anonymous · Answer

The question is asking me to complete the square for 2x^2+9x+4=0; help me please! this is my first time using service.

wolf1728 · Answer

2x² + 9x +4 =0

To complete the square: 
Move the "non X" term to the right: 
2x² + 9x  =-4

Divide the equation by the coefficient of X² 
x² + 4.5x = -2

take the coefficient of X and divide it by 2 then square it
4.5 / 2 = 2.25 and 2.25² = 5.0625

add 5.0625 to both sides of the equation
x² + 4.5x +5.0625= -2 +5.0625

Take square root of both sides
x + 2.25 = sqrt(3.0625)
x + 2.25 = 1.75
x = -.5

sqrt of 3.0625 also equals -1.75
x + 2.25 = -1.75
x = -4