Question

2x+2x^-1+2x^-2+2x^-3+2x^-4=496 then x=?

Answer 1

Answer:

Step-by-step explanation:

2(x-3)=2x^2-x+3

Simplifying

2(x + -3) = 2x2 + -1x + 3

Reorder the terms:

2(-3 + x) = 2x2 + -1x + 3

(-3 * 2 + x * 2) = 2x2 + -1x + 3

(-6 + 2x) = 2x2 + -1x + 3

Reorder the terms:

-6 + 2x = 3 + -1x + 2x2

Solving

-6 + 2x = 3 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:

-6 + -3 + 2x + x + -2x2 = 3 + -1x + 2x2 + -3 + x + -2x2

Combine like terms: -6 + -3 = -9

-9 + 2x + x + -2x2 = 3 + -1x + 2x2 + -3 + x + -2x2

Combine like terms: 2x + x = 3x

-9 + 3x + -2x2 = 3 + -1x + 2x2 + -3 + x + -2x2

Reorder the terms:

-9 + 3x + -2x2 = 3 + -3 + -1x + x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0

-9 + 3x + -2x2 = 0 + -1x + x + 2x2 + -2x2

-9 + 3x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0

-9 + 3x + -2x2 = 0 + 2x2 + -2x2

-9 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0

-9 + 3x + -2x2 = 0

Begin completing the square.  Divide all terms by

-2 the coefficient of the squared term:  

Divide each side by '-2'.

4.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.

4.5 + -1.5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:

4.5 + -4.5 + -1.5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0

0.0 + -1.5x + x2 = 0 + -4.5

-1.5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5

-1.5x + x2 = -4.5

The x term is -1.5x.  Take half its coefficient (-0.75).

Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.

-1.5x + 0.5625 + x2 = -4.5 + 0.5625

Reorder the terms:

0.5625 + -1.5x + x2 = -4.5 + 0.5625

Combine like terms: -4.5 + 0.5625 = -3.9375

0.5625 + -1.5x + x2 = -3.9375

Factor a perfect square on the left side:

(x + -0.75)(x + -0.75) = -3.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.