Solve: negative 1 over 2 x + 1 = -x + 8

Solution:

The given problem is written as:

-1/(2x + 1) = -x + 8

-1 = (-x + 8)(2x + 1)

-1 = (-x)(2x) + (8)(1) + (8)(2x) + (-x)(1)

-1 = -2x² + 8 + 16x - x

-1 = -2x² + 15x + 8

2x² - 15x - 9 = 0

The above equation is a quadratic equation of the form ax² + bx + c = 0 the roots of which are given by the formula:

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Hence the roots are:

\(\frac{-(-15)\pm \sqrt{(-15)^{2}-4(2)(-9)}}{2(2)}\)

= \(\frac{15\pm \sqrt{225 + 72}}{2(2)}\)

= \(\frac{15\pm \sqrt{297}}{4}\)

= \(\frac{15\pm 3\sqrt{33}}{4}\)

The roots are :

\(\frac{15+ 3\sqrt{33}}{4}\) and \(\frac{15- 3\sqrt{33}}{4}\).

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Solve: negative 1 over 2 x + 1 = -x + 8

Summary:

Solving negative 1 over 2 x + 1 = -x + 8 we get the values of x as \(\frac{15+ 3\sqrt{33}}{4}\) and \(\frac{15- 3\sqrt{33}}{4}\)