Answer:
x = [tex]\frac{5+\sqrt{17}i }{7}[/tex]
Step-by-step explanation:
7[tex]x^{2}[/tex] - 10[tex]x[/tex] = -6
All equations of the form [tex]ax^{2}[/tex] + [tex]bx[/tex] + x = 0 0 can be solved using the quadratic formula: [tex]\frac{-b±\sqrt{b^{2} - 4ac } }{2a}[/tex]. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
[tex]7x^{2}[/tex] - 10[tex]x[/tex] = -6
Add 6 to both sides of the equation.
7[tex]x^{2}[/tex] - 10[tex]x[/tex] - (-6) = -6 - (-6)
Subtracting −6 from itself leaves 0.
[tex]7x^{2}[/tex] - 10[tex]x[/tex] + 6 = 0
This equation is in standard form: [tex]ax^{2} + bx + c = 0.[/tex] Substitute 7 for a, −10 for b, and 6 for c in the quadratic formula, [tex]\frac{-b±\sqrt{b^{2 -4ac} } }{2a}[/tex]
[tex]x[/tex] =
[tex]\frac{-(-10) ± \sqrt{(-10)^{2}-4 x 7 x6 } }{2 x 7 }[/tex]
Square −10.
[tex]x[/tex] =
[tex]\frac{- (-10) ±\sqrt{100 - 4 x 7x 6} }{2x7}[/tex]
Multiply −4 times 7
[tex]x[/tex] =
[tex]\frac{- (-10)± \sqrt{100 - 28 x 6} }{2 x 7}[/tex]
Multiply −28 times 6
[tex]x[/tex] = [tex]\frac{-(-10)±\sqrt{100 - 168} }{2x 7}[/tex]
Add 100 to −168
[tex]x[/tex] = [tex]\frac{-(-10)±\sqrt{-68} }{2x7}[/tex]
Take the square root of −68.
[tex]x[/tex] = [tex]\frac{-(-10)± 2\sqrt{17i} }{2x7}[/tex]
The opposite of −10 is 10.
[tex]x[/tex] = [tex]\frac{10±2\sqrt{17i} }{2x7}[/tex]
Multiply 2 times 7.
[tex]x[/tex] = [tex]\frac{10±2\sqrt{17i} }{14}[/tex]
Now solve the equation [tex]x[/tex] = [tex]\frac{10±2\sqrt{17i} }{14}[/tex] when ± is plus. Add 10 to [tex]2i[/tex] [tex]\sqrt{17}[/tex].
[tex]x[/tex] = [tex]\frac{10+2\sqrt{17i} }{14}[/tex]
Divide 10 + [tex]2i[/tex][tex]\sqrt{17}[/tex] by 14
[tex]x[/tex] = [tex]\frac{5+\sqrt{17i} }{7}[/tex]
Now solve the equation [tex]x[/tex] = [tex]\frac{10+2\sqrt{17i} }{14}[/tex] when ± is minus. Subtract [tex]2i[/tex][tex]\sqrt{17}[/tex] from 10.
[tex]x[/tex] = [tex]\frac{-2\sqrt{17i}+10 }{14}[/tex]
Divide 10 - [tex]2i[/tex] [tex]\sqrt{17}[/tex] by 14
[tex]x[/tex] = [tex]\frac{-\sqrt{17}i +5 }{7}[/tex]
The equation is now solved.
[tex]x[/tex] = [tex]\frac{5+\sqrt{17i} }{7}[/tex]
Hope it helps and have a great day! =D
