Equations – Solving a polynomial equation – Exercise 5581


Solve the equation:


Final Answer

x=\pm 1



In order to get quadratic equation, we define a new variable:


We set the new variable:


It’s a quadratic equation with the coefficients:

a=5, b=3, c=-8

We solve it with the quadratic formula. Putting the coefficients in the formula gives us

y_{1,2}=\frac{-3\pm \sqrt{3^2-4\cdot 5\cdot (-8)}}{2\cdot 5}=

=\frac{-3\pm \sqrt{169}}{10}=

=\frac{-3\pm 13}{10}

Hence, we get the solutions:

y_1=\frac{-3+ 13}{10}=\frac{10}{10}=1

y_2=\frac{-3- 13}{10}=\frac{-16}{10}=-1.6

We go back to the original variable. From the first solution we get


x=\pm 1

From the second solution we get


This equation has no real solution, because the left side is negative, while the right side is positive for every x.

Hence, the only solution of the equation is

x=\pm 1

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