Question

Can someone help me pls (show work pls) and thank you

Answer 1

x =
`(5+√(17)i )/(7)`

Explanation:

7
`x^(2)` - 10
`x` = -6

All equations of the form
`ax^(2)` +
`bx` + x = 0 0 can be solved using the quadratic formula:
`\frac{-b±\sqrt{b^(2) - 4ac } }{2a}`. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

`7x^(2)` - 10
`x` = -6

Add 6 to both sides of the equation.

7
`x^(2)` - 10
`x` - (-6) = -6 - (-6)

Subtracting −6 from itself leaves 0.

`7x^(2)` - 10
`x` + 6 = 0

This equation is in standard form:
`ax^(2) + bx + c = 0.` Substitute 7 for a, −10 for b, and 6 for c in the quadratic formula,
`\frac{-b±\sqrt{b^(2 -4ac) } }{2a}`

`x` =

`\frac{-(-10) ± \sqrt{(-10)^(2)-4 x 7 x6 } }{2 x 7 }`

Square −10.

`x` =

`(- (-10) ±√(100 - 4 x 7x 6) )/(2x7)`

Multiply −4 times 7

`x` =

`(- (-10)± √(100 - 28 x 6) )/(2 x 7)`

Multiply −28 times 6

`x` =
`(-(-10)±√(100 - 168) )/(2x 7)`

Add 100 to −168

`x` =
`(-(-10)±√(-68) )/(2x7)`

Take the square root of −68.

`x` =
`(-(-10)± 2√(17i) )/(2x7)`

The opposite of −10 is 10.

`x` =
`(10±2√(17i) )/(2x7)`

Multiply 2 times 7.

`x` =
`(10±2√(17i) )/(14)`

Now solve the equation
`x` =
`(10±2√(17i) )/(14)` when ± is plus. Add 10 to
`2i`
`√(17)`.

`x` =
`(10+2√(17i) )/(14)`

Divide 10 +
`2i`
`√(17)` by 14

`x` =
`(5+√(17i) )/(7)`

Now solve the equation
`x` =
`(10+2√(17i) )/(14)` when ± is minus. Subtract
`2i`
`√(17)` from 10.

`x` =
`(-2√(17i)+10 )/(14)`

Divide 10 -
`2i`
`√(17)` by 14

`x` =
`(-√(17)i +5 )/(7)`

The equation is now solved.

`x` =
`(5+√(17i) )/(7)`

Hope it helps and have a great day! =D