   Chapter 11.2, Problem 34E

Chapter
Section
Textbook Problem

Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 18.9 x 2 − 44.2 x = 21.5

To determine

To calculate: The solution of the equation 18.9x244.2x=21.5 by the use of quadratic formula.

Explanation

Given Information:

The given equation, 18.9x244.2x=21.5.

Formula used:

The quadratic equation in the form ax2+bx+c=0, the roots of the equation can be calculated by quadratic formula,

x=b±b24ac2a

Where, the coefficient of x2 is a, the coefficient of the term x is b, and the constant term is c.

Calculation:

Consider the equation,

18.9x244.2x=21.5

Rewrite the equation in the general form as below,

18.9x244.2x21.5=0

Compare the equation with the standard quadratic equation ax2+bx+c=0.

So, the values are a=18.9,b=44.2 and c=21.5.

Now, substitute the values of a, b and c, in the quadratic formula,

x=b±b24ac2a=(44.2)±(44.2)24(18.9)(21.5)2(18.9)=44.2±1953.64+1625.437.8=44.2±3579.0437.8

Solve further,

x=44

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