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Solve the Quadratic Equation.

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Lesson Parent:

Problem:

Solve the Quadratic Equation. In other words, find the two values of $x$ for which $ax^2+bx+c=0$ is true.

Answer:

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

Solution:

Because <Sign in to see all the formulas> we can divide both sides by $a$ to get

and then subtract $c/a$ from both sides to get

Next we are going to add <Sign in to see all the formulas> to both sides to get

The reason we did this is because we now have a perfect square on the left-hand side of the equation. That means

We can also reorganize the right-hand side as well to get

Now because the square root of a number has two solutions (<Sign in to see all the formulas> and <Sign in to see all the formulas>) we see that