![]() Rewrite the perfect square on the left to the form (x + y) 2.Add this result to both sides of the equation.Take the b term, divide it by 2, and then square it.Move the c term to the right side of the equation by subtracting it from or adding it to both sides of the equation.Your b and c terms may be fractions after this step. If a ≠ 1, divide both sides of your equation by a.First, arrange your equation to the form ax 2 + bx + c = 0.It takes a few steps to complete the square of a quadratic equation. If it is not 1, divide both sides of the equation by the a term and then continue to complete the square as explained below. You can use the complete the square method when it is not possible to solve the equation by factoring.įirst, make sure that the a term is 1. What is Completing the Square?Ĭompleting the square is a method of solving quadratic equations by changing the left side of the equation so that it is the square of a binomial. Get instantaneous results! Our calculator handles any quadratic equation quickly, saving you time and effort.The solution shows the work required to solve a quadratic equation for real and complex roots by completing the square. This feature makes it an excellent learning tool for those trying to understand the process behind the calculation. Not only does this calculator give you the discriminant value, but it also provides a step-by-step solution. Just input your quadratic equation, and the tool will do the rest. With a straightforward and user-friendly interface, our Discriminant Calculator is easy to use. The calculator ensures that all calculations are error-free, delivering accurate results every time. For example, in the equation $$$x^2+4=0 $$$, the discriminant is $$$-16 $$$ (a negative number), so there are two complex solutions, namely, $$$x=\pm2i $$$. This means the parabola does not intersect the x-axis at all. Instead, it has two complex roots (solutions). When the discriminant is negative, the quadratic equation has no real roots. ![]() ![]() Negative Discriminant $$$\left(D\lt0\right) $$$ ![]() For example, in the equation $$$x^2-6x+9=0 $$$, the discriminant is $$$0 $$$, so there is one real solution (or two identical real solutions), namely, $$$x=3 $$$. In other words, the parabola touches the x-axis at exactly one point. When the discriminant is zero, the quadratic equation has exactly one real root or two real roots that are the same (also known as repeated roots). Zero Discriminant $$$\left(D=0\right) $$$ For example, in the equation $$$x^2-5x+6=0 $$$, the discriminant is $$$1 $$$ (a positive number), so there are two real and distinct solutions, namely, $$$x=2 $$$ and $$$x=3 $$$. This means the parabola represented by the equation crosses the x-axis at two distinct points. The quadratic equation has two distinct real roots when the discriminant is positive. Positive Discriminant $$$\left(D\gt0\right) $$$ In the context of a quadratic equation, the discriminant, represented by the formula $$$D=b^2-4ac $$$, carries crucial information about the nature of the roots (solutions) of the equation. What Does a Positive and Negative Discriminant Represent? Since $$$D\gt0 $$$, this equation has two distinct real roots. Substituting these values into the discriminant formula gives: $$D=(-6)^2 - 4\cdot2\cdot3=36-24=12 $$ Consider the quadratic equation $$$2x^2-6x+3=0 $$$. The discriminant $$$D $$$ of this equation is given by the formula: $$D=b^2-4ac $$ The general form of a quadratic equation is: $$ax^2+bx+c=0, $$ A quadratic equation is a second-order polynomial equation in a single variable $$$x $$$, with a non-zero coefficient for $$$x^2 $$$. In algebra, the discriminant plays a crucial role in determining the nature of the roots of a quadratic equation. The calculator will calculate the discriminant.Īfter the calculation, the Discriminant Calculator will display the discriminant value instantly on the screen. Once you've entered the coefficients, click on the "Calculate" button. Make sure you enter it correctly to get accurate results. Input your quadratic equation in the designated field. By computing the discriminant, you gain insights into the character of the roots of the quadratic equation. Our Discriminant Calculator is an efficient and potent tool to assist you in effortlessly calculating the discriminant. During your algebra exploration, you'll inevitably encounter quadratic equations.
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