Quadratic Formula Calculator

\(a =\)
\(b =\)
\(c =\)
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The quadratic formula helps you solve equations with x² terms. It works for equations that look like ax² + bx + c = 0, where a isn’t zero. Here’s the formula:

x = (-b ± √(b² – 4ac)) / (2a)

This formula gives you the x-values that make the equation true. You might get one answer, two answers, or complex numbers as answers.

Solving Quadratic Equations Step-by-Step

Let’s look at how to use the quadratic formula:

  1. Identify a, b, and c in your equation.
  2. Put these values into the formula.
  3. Solve the math inside the square root.
  4. Add and subtract to find both possible answers.

Example: Solve x² – 8x + 5 = 0

Here, a = 1, b = -8, and c = 5.

x = (8 ± √((-8)² – 4(1)(5))) / (2(1)) x = (8 ± √(64 – 20)) / 2 x = (8 ± √44) / 2 x = 4 ± √11

So, x ≈ 7.32 or 0.68

You can check your work by plugging these x-values back into the original equation.

Tips:

  • If b² – 4ac is positive, you’ll get two real answers.
  • If it’s zero, you’ll get one real answer.
  • If it’s negative, you’ll get complex answers.

The quadratic formula always works, but sometimes factoring is faster. Try factoring first if the numbers look friendly. Use the formula when factoring seems tough.