Solve the following quadratic equation by completing the square.

Question

Quizplus · Accepted Answer

The quadratic equation is in the form of:

$$ax^2+bx+c=0$$

We need to complete the square to solve this equation.

First, divide both sides by $a$ to get:

$$x^2+\frac{b}{a}x+\frac{c}{a}=0$$

Next, we need to add and subtract $(b/2a)^2$ inside the brackets:

$$x^2+\frac{b}{a}x+\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2+\frac{c}{a}=0$$

The first three terms inside the brackets form a perfect square:

$$\left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{c}{a}=0$$

Simplifying, we get:

$$\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}$$

Taking the square root of both sides, we get:

$$x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}$$

Solving for $x$, we get:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Therefore, the correct choice is B.

Solve the Following Quadratic Equation by Completing the Square