Question

Beginning with the general form of a quadratic equation. ax^2+bx+c=0, solve for x by using the completing the square method, thus deriving the quadratic formula. To earn full credit be sure to show all steps/calculations. You may want to do the work by hand and upload a picture of that written work rather than try to type it out.

Answer 1

to solve ax^2 + bx + c = 0 using completing the square method

divide all terms by a so as to reduce the coefficient of x^2 to 1

x^2 + bx/a + c/a = 0

subtract the constant term from both sides of the equation

x^2 + bx/a = -c/a

to have a square on the left sie the third term (constant) should be

(b/2a)^2

so add that amount to both side

x^2 + bx/a + (b/2a)^2 = (b/2a)^2 - c/a

rewrite the left side as a square

(x + (b/2a))^2 = (b/2a) - c/a

take the square root of both sides

x + (b/2a) = + square root of (b/2a)^2 - c/a

subtract the constant term on the left side from both sides

`\begin{gathered} x\text{ = }\pm\sqrt[]{((b)/(2a)})^2\text{ - c/a - (b/2a)} \\ x\text{ = -b }\pm\sqrt[]{\frac{b^2\text{ - 4ac}}{2a}} \end{gathered}`