   Chapter A.5, Problem 34E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

To find the length of C P ¯ (which is x), one must solve the equation x ⋅ ( x + 5 ) = ( x + 1 ) ⋅ 4 Find the length of C P ¯ .

To determine

To find:

To find the length of CP¯.

Explanation

Consider the following figure,

By using the above figure the equation become the following,

x(x+5)=(x+1)4

Then simplify the above expression by multiplying on both sides to get the following,

x(x+5)=(x+1)4x2+5x=4x+4

Then subtract 4x+4 on both sides to get the following,

x2+5x(4x+4)=4x+4(4x+4)x2+5x4x4=4x+44x4x2+x4=0

The general form of the quadratic equation is given below,

ax2+bx+c=0

Where a is the number multiplied by x2, b is the number multiplied by x, and c is the constant term.

The solution for ax2+bx+c=0 when a0 is given below,

x=b±b24ac2a..........(1)

Compare the given equation with general equation to get the following,

ax2+bx+c=0x2+x4=0

Therefore,

a=1,b=1 and c=4

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