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In the following exercises, solve.

15x-2-26x-1+8=0

Short Answer

Expert verified

The solutions of the given equation are x=52and localid="1644991122921" x=34.

Step by step solution

01

Step 1. Write the equation in standard form.

The given equation is:

15x-2-26x-1+8=0

It can be written as:

15(x-1)2-26x-1+8=0

Substitute x-1=u.

15u2-26u+8=0

02

Step 2. Solve the equation.

Split the middle term.

15u2-20u-6u+8=05u(3u-4)-2(3u-4)=0(5u-2)(3u-4)=0u=25andu=43

Substitute u=x-1.

localid="1644991105556" x-1=25andx-1=43x=52andx=34

03

Step 3. Conclusion.

The solutions of the given equation are x=52and localid="1644991088222" x=34.

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