Babylonian mathematicians as early as the Sumerian Ur III period (21st to 20th century B.C.) used geometric methods to solve second-degree problems. Similar geometric methods solved quadratic equations in later Babylonia, Egypt, Greece, China, and India. Indian mathematician Brahmagupta (597-668 C.E.) was the first to give an explicit solution.Know More
Ancient Babylonians understood second-degree equations as geometric problems of sides and areas of rectangles and squares. The equation can be geometrically stated as saying that if a rectangle with sides of the length s and f/2 * s is removed from a rectangle with sides p and s, then the remainder is a rectangle of given area B. Euclid summarized these geometric solutions in Book II of the Elements where he represented such problems by a combination of rectangles and lines.
Brahmagupta of India was instrumental in understanding that numbers are abstract concepts which can be zero or negative. He pointed out that quadratic equations can have two possible solutions, one of which can be negative. He derived algebraic solutions to quadratic equations and went several steps further by solving systems of equations and quadratic equations with two unknowns. The latter was not considered by European mathematicians until more than a millennium later.Learn more about Algebra
To solve the quadratic equation ax^2 + bx + c - 0, plug the corresponding numbers into the quadratic formula. Take the opposite of b, and provide the option of adding or subtracting the square root of (b^2 - 4ac). Divide the result by 2a.Full Answer >
In math, expanded form can refer to any type of expression, equation or notation that is completely broken down into its individual parts. Expanded form is commonly used in teaching students place value and factoring.Full Answer >
The general equation of a circle in the Cartesian coordinate system is (x-a)2 + (y-b)2 = r2. The point (a,b) represents the center of the circle and the value of r represents the radius of the circle.Full Answer >
To solve by factoring, move all terms to the same side of the equation with subtraction or addition, and then find each factor in the equation. Setting each factor at zero provides all of the solutions to the equation.Full Answer >