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-x^2+4x+3=x^2-x-(1+2x^2)

-x^2+4x+3=x^2-x-(1+2x^2) equation

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Numerical solution:

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The solution

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   2              2               2
- x  + 4*x + 3 = x  - x + -1 - 2*x 
$$\left(- x^{2} + 4 x\right) + 3 = \left(- 2 x^{2} - 1\right) + \left(x^{2} - x\right)$$
Detail solution
Given the linear equation:
-x^2+4*x+3 = x^2-x-(1+2*x^2)

Expand brackets in the right part
-x^2+4*x+3 = x^2-x-1-2*x-2

Looking for similar summands in the right part:
3 - x^2 + 4*x = -1 - x - x^2

Move free summands (without x)
from left part to right part, we given:
$$- x^{2} + 4 x = - x^{2} - x - 4$$
Move the summands with the unknown x
from the right part to the left part:
$$- x^{2} + 5 x = - x^{2} + -4$$
Divide both parts of the equation by (-x^2 + 5*x)/x
x = -4 - x^2 / ((-x^2 + 5*x)/x)

We get the answer: x = -4/5
The graph
Sum and product of roots [src]
sum
-4/5
$$- \frac{4}{5}$$
=
-4/5
$$- \frac{4}{5}$$
product
-4/5
$$- \frac{4}{5}$$
=
-4/5
$$- \frac{4}{5}$$
-4/5
Rapid solution [src]
x1 = -4/5
$$x_{1} = - \frac{4}{5}$$
x1 = -4/5
Numerical answer [src]
x1 = -0.8
x1 = -0.8
The graph
-x^2+4x+3=x^2-x-(1+2x^2) equation