Does x = -1 Solve the Equation x^2 + 2x = -1

The best method to solve the equation is by completing the square. Step 1: Keep all terms containing $ x $ on one side. Move $ -1 $ to the right.$$ x^2-2x = 1 $$

Although we can see by inspection that the solution is 9, because -(9) = -9, we can avoid the negative coefficient by adding -2x and +9 to each member of Equation (1). In this case, we get ... from which the solution 9 is obvious. If we wish, we can write the last equation as x = 9 by the symmetric ...

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Use the quadratic formula to find the solutions.

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In fact this requires to consider 2 relations within their appropriate realm. $$x^2+x-1=0\ for\ x\ge 1$$ $$x^2-x+1=0\ for\ x<1$$ ... Dr. Richard Klitzing · 5,8151111 silver badges1717 bronze badges $\endgroup$ ... Then the equation becomes $x^2+x-1=0$ for which $x = -.5\pm 1.118 \le 1$ and hence no solution because $x \gt 1$

The equation has no real solution because $2x - 2x^2 - 1 = -(x-1)^2-x^2 < 0$ for all $x\in\mathbb R$.

Did you notice anything strange about the above solution? That’s right: the numbers inside the square roots are negative! As a decimal, x is roughly 1.088 metres. But that’s not the point. The point is that x is the sum of two complex numbers. We need complex numbers to solve a real-life problem that has nothing to do with complex numbers.