Solve a quadratic with the quadratic formula
When an equation is in quadratic form, a reliable way to find its solutions is to use the quadratic formula:
[
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
]
where the equation has been written as (ax^2+bx+c=0).
Steps
- Put the equation in standard form.
Move all terms to one side so the right side is 0.
- Identify (a), (b), and (c).
Be careful with signs, especially when a term is negative.
- Substitute into the formula.
Replace (a), (b), and (c) in the formula.
- Simplify the discriminant.
Compute (b^2-4ac) first, then simplify the square root.
- Find both solutions.
Use both the plus and minus signs, since a quadratic can have two real solutions, one real repeated solution, or no real solution.
Check your answer
Substitute each solution back into the original equation. If both sides match, the solution is correct. If the result is not exact, leave the answer in simplified exact form unless the instructions ask for decimals.