The quadratic formula calculator helps you to find the roots of the quadratic equation and shows step-by-step calculations. Our free online tool gives explicit results by optimizing the use of resources.
The Latin word “quadratic” comes from quadratum, generally used for square.
Our quadratic equation solver helps you to reduce the following second-degree expression to its roots:
$$ ax^2 + bx + c = 0 $$
Where,
$$ \dfrac{a}{a}x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0 $$
$$ x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0 $$
$$ x^2 + \dfrac{b}{a}x = -\dfrac{c}{a} $$
Add $$ (\frac{b}{2a})^2 $$ on both sides of the equation.
$$ x^2 + \dfrac{b}{a}x + (\dfrac{b}{2a})^2 = -\dfrac{c}{a} + (\dfrac{b}{2a})^2 $$
$$ (x + \dfrac{b}{2a})^2 = -\dfrac{c}{a} + \dfrac{b^2}{4a^2} $$
$$ (x + \dfrac{b}{2a})^2 = \dfrac{b^2 – 4ac}{4a^2} $$
Take a square root on both sides of the equation.
$$ \sqrt{(x + \dfrac{b}{2a})^2} = \pm \sqrt{\dfrac{b^2 – 4ac}{4a^2}} $$
$$ x + \dfrac{b}{2a} = \pm \dfrac{\sqrt{b^2 – 4ac}}{2a} $$
$$ x = -\dfrac{b}{2a} \pm \dfrac{\sqrt{b^2 – 4ac}}{2a} $$
$$ x = \dfrac{-b \pm \sqrt{b^2 – 4ac}}{2a} $$
The quadratic formula calculator helps you to solve any quadratic equation in a matter of seconds. However, if your goal comes up with the manual calculations, you must delve into the example to explore more.
Suppose that we have 3x^2 - 5x + 2 = 0. We need to solve by the quadratic equation formula.
We already know about the formula that is:
$$ x = \dfrac{-b \pm \sqrt{b^2 – 4ac}}{2a} $$
And we also know the values of a, b, and c in the above-given statement:
a= 3, b= -5, and c= 2
Put the values in the formula.
$$ x = \dfrac{-5 \pm \sqrt{-5^2 – 4(3)(2)}}{2(3)} $$
$$ x = \dfrac{5 \pm \sqrt{25 – 24)}}{6} $$
$$ x = \dfrac{5 \pm \sqrt{1}}{6} $$
Here the roots of a quadratic equation have two solutions.
Root # 1
$$ x = \dfrac{5+1}{6} $$
$$ x =\dfrac{6}{6} $$
$$ x = 1 $$
Root # 2
$$ x = \dfrac{5-1}{6} $$
$$ x = \dfrac{4}{6} $$
$$ x = \dfrac{2}{3} $$
To learn more about quadratic equations and their calculations, find our complete quadratic tutorial for free.
The quadratic root calculator will help you carry out calculations easily! Just enter the required values. Our quadratic function calculator will work best for you!
Input:
Output:
There are three possibilities which include:
No, It is just used to solve the quadratic equations that are in the form of $$ ax^2 + bx + c = 0 $$. This form is also known as the standard form of the quadratic formula calculator.
A second-degree equation formula equation has two roots. It depends on the degree of the equation.
From the source Wikipedia: Quadratic equation, Solving the quadratic equation, Examples, and applications, History, Advanced topics
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