QUADRATIC EQUATIONS.203XIX. QUADRATIC EQUATIONS.339. A Quadratic Equation is an equation of the second degree (Art. 179), containing but one unknown quantity.A Pure Quadratic Equation is a quadratic equation involving only the square of the unknown quantity ;An Affected Quadratic Equation is a quadratic equation involving both the square and the first power of the unknown quantity ; as, 2x* - 3 x - 5 = 0.PURE QUADRATIC EQUATIONS.340. A pure quadratic equation may be solved by reducing it, if necessary, to the form x2 = a, and then extracting the square root of both members.5 a,"21. Solve the equation 3 x2 + 7 = + 35.Clearing of fractions, 12 x2 + 28 = 5 x2 +140.Transposing and uniting, 7 x2 = 112, or, x2 = 16 ;which is in the form x2 = a.Extracting the square root of both members, we havea = ±4. (Notes 1 and 2.)Note 1. The sign ± is placed before the result, because the square root of a number is either positive or negative (Art. 236).Note 2. ITable of Contents CONTENTS; PAGE; I Definitions and Notation 1; II Fundamental Operations 9; III Addition ; Subtraction ; Use of Parentheses 24; IV Multiplication 29; V Division 36; VI Formulae 41; VII Factoring 50; VIII Highest Common Factor 59; IX Lowest Common Multiple 66; X Fractions 70; XI Simple Equations containing one Unknown; Quantity 85; XII Simple Equations containing two or more; Unknown Quantities 98; XIII Discussion of Simple Equations 113; XIV Inequalities 124; XV Involution 130; XVI- Evolution 136; XVII Surds; the Theory of Exponents 1G4; XVIII Imaginary Numbers 100; XIX Quadratic Equations 203; XX Theory of Quadratic Equations 221; XXI Problems involving Quadratic Equations 234 XXII Equations Solved like Quadratics 239 XXIIT Simultaneous Equations involving Quadratics 246; XXIV Indeterminate Equ