Then, we do all the math to simplify the expression. To use the Quadratic Formula, we substitute the values of a, b, and c into the expression on the right side of the formula. One conjecture is that the proof by similar triangles involved a theory of proportions, a topic not discussed until later in the Elements, and that the theory of proportions needed further development at that time. The solutions to a quadratic equation of the form ax2 + bx + c 0, a 0 are given by the formula: x b ± b2 4ac 2a. All terms originally had a common factor of 2, so we divided all sides by 2 the zero side remained zerowhich made the factorization easier. The underlying question is why Euclid did not use this proof, but invented another. This is how the solution of the equation 2 x 2 12 x + 18 0 goes: 2 x 2 12 x + 18 0 x 2 6 x + 9 0 Divide by 2. The role of this proof in history is the subject of much speculation. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: a 2 + b 2 = c 2. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Here we will learn about the quadratic equation and how to solve quadratic equations using four methods: factorisation, using the quadratic equation formula, completing the square and using a graph.
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