Question 362564
 (should be x - squared, and 8x to -1 power) 

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{{{x^-2 + 8x^-1 = -10}}}
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Sub y for x^-1
{{{y^2 + 8y + 10 = 0}}}
*[invoke solve_quadratic_equation 1,8,10]
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The solutions shown are for y.
y = -4 ± sqrt(6)
1/x = = -4 ± sqrt(6)
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x = 1/(-4 + sqrt(6))
x = (-4 - sqrt(6))/(16 - 6)
x = (-4 ± sqrt(6))/10
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Substitution is not the best method, tho.
{{{x^-2 + 8x^-1 = -10}}}
Multiply thru by x^2
{{{1 + 8x = -10x^2}}}
{{{10x^2 + 8x + 1 = 0}}}
*[invoke solve_quadratic_equation 10,8,1]
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Simpler, less work, less time.