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(0.9649-1.0008)/(1.4-1.6)=(0.9649-x)/(1-1.416) equation

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Numerical solution:

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The solution

You have entered [src]
-0.0358999999999999   0.9649 - x
------------------- = ----------
     7/5 - 8/5             177  
                       1 - ---  
                           125  
$$- \frac{0.0358999999999999}{- \frac{8}{5} + \frac{7}{5}} = \frac{0.9649 - x}{- \frac{177}{125} + 1}$$
Detail solution
Given the linear equation:
(0.9649-1.0008)/((7/5)-(8/5)) = (0.9649-x)/(1-(177/125))

Expand brackets in the left part
0.9649-1.00087/5-8/5) = (0.9649-x)/(1-(177/125))

Expand brackets in the right part
0.9649-1.00087/5-8/5) = 0.9649-x1+177/125)

Looking for similar summands in the left part:
0.1795 = 0.9649-x1+177/125)

Move free summands (without x)
from left part to right part, we given:
$$-3.33066907387547 \cdot 10^{-16} = \frac{125 x}{52} - 2.49897115384615$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-125\right) x}{52} - 3.33066907387547 \cdot 10^{-16} = -2.49897115384615$$
Divide both parts of the equation by (-3.33066907387547e-16 - 125*x/52)/x
x = -2.49897115384615 / ((-3.33066907387547e-16 - 125*x/52)/x)

We get the answer: x = 1.03957200000000
The graph
Sum and product of roots [src]
sum
1.03957200000000
$$1.039572$$
=
1.03957200000000
$$1.039572$$
product
1.03957200000000
$$1.039572$$
=
1.03957200000000
$$1.039572$$
1.03957200000000
Rapid solution [src]
x1 = 1.039572
$$x_{1} = 1.039572$$
x1 = 1.039572
Numerical answer [src]
x1 = 1.039572
x1 = 1.039572