Given x-3=-5/x find all solutions for x, please go step by step, thanks.
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x-3 = -5/x
Multiply both sides by x
x^2 - 3x = -5
Get in quadratic form:
x^2 - 3x +5 =0
For a quadratic equation in the form ax^2 + bx + c = 0 (in this case a=1, b=-3, c=5), the solutions are:
x = (-b +/- sqrt(b^2 - 4ac)) / (2*a)
x = (3 +/- sqrt((-3)^2 - 4*1*5)) / (2*1)
x = (3 +/- sqrt(9 - 20) ) / 2
x = (3 +/- sqrt(-11) ) / 2
x = (3 +/- i*sqrt(11) ) / 2 -- note: sqrt(-1) = i, the imaginary number
x = 3/2 + i*sqrt(11)/2 or 3/2 - i*sqrt(11)/2
Multiply both sides by x
x^2 - 3x = -5
Get in quadratic form:
x^2 - 3x +5 =0
For a quadratic equation in the form ax^2 + bx + c = 0 (in this case a=1, b=-3, c=5), the solutions are:
x = (-b +/- sqrt(b^2 - 4ac)) / (2*a)
x = (3 +/- sqrt((-3)^2 - 4*1*5)) / (2*1)
x = (3 +/- sqrt(9 - 20) ) / 2
x = (3 +/- sqrt(-11) ) / 2
x = (3 +/- i*sqrt(11) ) / 2 -- note: sqrt(-1) = i, the imaginary number
x = 3/2 + i*sqrt(11)/2 or 3/2 - i*sqrt(11)/2
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x^2-3x=-5
x^2-3x+5
x=1.5+1.65831i or1.5-1.65831i
x^2-3x+5
x=1.5+1.65831i or1.5-1.65831i