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So, we are told that f of x isĮqual to x minus two squared minus nine. That's presented to us in a slightly different way. So, these are the two possible x-values that satisfy the equation. And when x is equal to negative five, negative five plus three is negative two, squared is positive four, minusįour is also equal to zero. You substitute it back in if you substitute x equals negative one, then x plus three is equal to two, two-squared is four, minus four is zero. Substitute it back in, and then you can see when So, those are the two possible solutions and you can verify that. Negative two minus three is negative five. Or, over here we could subtract three from both sides to solve for x. Sides to solve for x and we're left with x isĮqual to negative one. So, if x plus three isĮqual to two, we could just subtract three from both If x plus three was negative two, negative two-squared is equal to four. Notice, if x plus three was positive two, two-squared is equal to four. And so we could write that x plus three couldīe equal to positive two or x plus three could beĮqual to negative two. Positive square root of four or the negative square root of four.
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Something right over here, is going to be equal to the If something-squared is equal to four, that means that the something, that means that this Three is going to be equal to the plus or minus So, one way of thinking about it is, I'm saying that x plus Way of thinking about it, if I have something-squared equaling four, I could say that that something needs to either be positive or negative two. And so now, I could take the square root of both sides and, or, another So, x plus three squared is equal to four. So, adding four to both sides will get rid of thisįour, subtracting four, this negative four on the left-hand side. This is I'm gonna isolate the x plus three squared on one side and the best way to do that Our calculator provides immediate solutions, allowing users to quickly move on to other tasks or verify their manual calculations without delay.The video and see if you can solve for x here. We've developed a simple and intuitive interface that even those new to quadratic equations can easily navigate.
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Whether your equation has real or complex roots, our tool delivers the correct solution. Our calculator is equipped with advanced algorithms that ensure the results are accurate every time. Why Choose Our Quadratic Equation Calculator? If $$$b^2-4ac\lt0 $$$, the equation has two complex roots.If $$$b^2-4ac=0 $$$, there's one real root (a repeated root).If $$$b^2-4ac\gt0 $$$, the equation has two distinct real roots.The term inside the square root is called the discriminant. The quadratic formula is a universal method to find the roots or solutions of any quadratic equation. Depending on the values of $$$a $$$, $$$b $$$, and $$$c $$$, the parabola can open upwards or downwards and have its vertex anywhere in the coordinate plane. The graphical representation of a quadratic function is a parabola.
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It's essential that $$$a\ne0 $$$, otherwise, the equation will not be quadratic but linear.$$$x $$$ is the variable or the unknown we aim to find.It has the following form: $$ax^2+bx+c=0, $$ A quadratic equation can have one of three types of roots: two distinct real roots, one repeated real root, or two complex roots.Ī quadratic equation is a particular type of polynomial equation of the second degree. In a short moment, the calculator will show the roots. The calculator will quickly determine the solutions of the equation. How to Use the Quadratic Equation Calculator?Įnter the given quadratic equation and choose the method for solving it.Īfter entering the equation, click the "Calculate" button. Welcome to the ultimate online Quadratic Equation Calculator! Our tool helps you solve quadratic equations with ease, giving you the most accurate results using the quadratic formula.