# Objectives: Solve equations of the form ax 2 = k. Solve equations of the form ax 2 = k where x is replaced by an algebraic expression. Standard Addressed:

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Objectives: Solve equations of the form ax 2 = k. Solve equations of the form ax 2 = k where x is replaced by an algebraic expression. Standard Addressed: 2.8.11.N. Solve quadratic equations.

 The equation x 2 = 9 can be stated as the question, “What number multiplied by itself is 9?” There are two such numbers, 3 and -3. Each of these is called a square root of 9. The positive square root of a number is called the principal square root. The principal square root of a number is indicated by the radical sign. In general, if x 2 = k and k > 0, then x = You can write this as, which is read as “plus or minus the square root of k.”

 x 2 = 100 x = 10, -10  d. 4x 2 = 25 x = 5/2, - 5/2  e. 49x 2 = 16 x = 4/7, -4/7

 (x + 7) 2 = 81  x + 7 = 9 x + 7 = -9  x = 2x = -16

 4x 2 = 240  X 2 = 60  X = 7.75, -7.75

 5x 2 = 250  x 2 = 50  X = 7.07, -7.07

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