Question

If you complete the square in the quadratic equation ​, you get the quadratic formula for the solutions x ​_______.

Answer 1

`D. \ \ x=\frac{-b\pm \sqrt{b^(2)-4ac} }{2a}`

Explanation:

ax² + bx + c = 0

`a\left( x^(2)+(b)/(a) x+(c)/(a) \right) =0`

`a\left( \left( x+(b)/(2a) \right)^(2) -(b^(2))/(4a^2)+(c)/(a) \right) =0`

`a\left( \left( x+(b)/(2a) \right)^(2) -(b^(2)-4ac)/(4a^2)\right) =0`

`a\left( x+(b)/(2a) \right)^(2) -(b^(2)-4ac)/(4a)=0`

`a\left( x+(b)/(2a) \right)^(2) =(b^(2)-4ac)/(4a)`

`\left( x+(b)/(2a) \right)^(2) =(b^(2)-4ac)/(4a^2)`

`x+(b)/(2a) =\frac{\pm \sqrt{b^(2)-4ac} }{2a}`

`x=\frac{-b\pm \sqrt{b^(2)-4ac} }{2a}`