Download 10.2 Solving Equations by Using Square Roots

Objectives: Solve equations of the form ax2 = k.
Solve equations of the form ax2 = k where x is
replaced by an algebraic expression.
Standard Addressed: 2.8.11.N. Solve quadratic
equations.
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The equation x2 = 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 x2= k and k > 0,
then x =
You can write this as
,
which is read as “plus or minus the square
root of k.”
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x2 = 100
x = 10, -10
d. 4x2 = 25
x = 5/2, - 5/2
e. 49x2 = 16
x = 4/7, -4/7
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(x + 7)2 = 81
x+7=9
x=2
x + 7 = -9
x = -16
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4x2 = 240
X2 = 60
X = 7.75, -7.75
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5x2 = 250
x2 = 50
X = 7.07, -7.07