Quadratic Formula Calculator

Free online calculator for quadratic equation solver. Quadratic Formula Calculator is a Quadratic Equation Solver to solve a second-order polynomial equation such as ax2 + bx + c = 0. Solve quadratic equations using this Quadratic Formula Calculator along with the work.

Explore other calculators or unit converters or try out our Quadratic Formula Calculator and learn more about Quadratic Formula .

Formula
ax2+bx+c=0ax^2 + bx + c = 0
a
b
c
Solution:
Solution will be shown here.

Quadratic Formula Calculator Details


Quadratic Formula Calculator is a Quadratic Equation Solver to solve a second-order polynomial equation such as a 2 + b + c = 0 for x where a ≠ 0, using the  quadratic formula and completing the square method.

Quadratic Formula Method

The quadratic formula =(− ±√( 2−4 ))/2  is used to solve quadratic equations where a ≠ 0 (polynomials with an order of 2) ax2 + bx + c = 0.

In the quadratic formula, the expression underneath the square root sign is called the discriminant of the quadratic equation.

Δ = b2 – 4ac

  • If the discriminant is zero, then there is exactly one real root

= (− /2 )

  • If the discriminant is positive, then there are two distinct roots

= (− + √Δ)/2   and = (− – √Δ)/2

  • If the discriminant is negative, then there are no real roots. Rather, there are two distinct (non-real) complex roots. i is the imaginary unit.

= − /2 + i(√-Δ)/2a   and =− /2 – i(√-Δ)/2a

Completing the Square

Completing the square method is where we take a Quadratic Equation like a 2 + b + c = 0  and turn it into a( + d)2 + e = 0. This method uses the algebraic formula (a+b)2 = a2 + b2 + 2ab

Steps to convert a 2 + b + c = 0 into a( + d)2 + e = 0.

  1. Divide each side by a, the coefficient of the squared term.
  2. Subtract the constant term c/a from both sides. Add the square of one-half of b/a, the coefficient of x, to both sides.
  3. This “completes the square”, converting the left side into a perfect square.