Question

Write a quadratic equation and solve it by completing the square. Show your work.

Answer 1

Answer:

Let the quadratic equation be  $2x^2 +12x+ 6$

Step 1: Take the coefficients of the $x^2$ term and divide the entire equation

Here the coefficient of $x^2$ is 2

So  dividing the entire equation by 2, we get

$x^2 +6x+ 3$

Step 2:  Move the constant term to the right side of the equation

$x^2 +6x = - 3$

Step 3: Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation

$(\frac{b}{2})^2$ =  $(\frac{6}{2})^2$ = $(3)^2$  =  9

$x^2 +6x + 9 = - 3 +9$

$(x+3)^2 = 6$

Step 4: Take the square root on both sides of the equation

$(x+3) = \sqrt{6}$

$x+3 = \pm 2.45$

Step 5 Subtract 3 from both sides:

$x+3 - 3 = \pm 2.45 -3$

$x = \pm 2.45 -3$

x =  2.45 - 3   or x = -2.45 - 3

x = - 0.55  or  x = -5.45