3x2 + 5x - 7x + 3 - 5x2 + 2

Simplifying

3x2 + 5x + - 7x + 3 + - 5x2 + 2 = 0

Reorder the terms:

3 + 2 + 5x + - 7x + 3x2 + - 5x2 = 0

Combine like terms: 3 + 2 = 5

5 + 5x + - 7x + 3x2 + - 5x2 = 0

Combine like terms: 5x + - 7x = - 2x

5 + - 2x + 3x2 + - 5x2 = 0

Combine like terms: 3x2 + - 5x2 = - 2x2

5 + - 2x + - 2x2 = 0

Solving

5 + - 2x + - 2x2 = 0

Solving for variable 'x'.

Begin completing the square. Divide all terms by

-2 the coefficient of the squared term:

Divide each side by '-2'.

-2.5 + x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.

-2.5 + x + 2.5 + x2 = 0 + 2.5

Reorder the terms:

-2.5 + 2.5 + x + x2 = 0 + 2.5

Combine like terms: - 2.5 + 2.5 = 0.0

0.0 + x + x2 = 0 + 2.5

x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5

x + x2 = 2.5

The x term is x. Take half its coefficient (0.5).

Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.

+ 0.25 + x2 = 2.5 + 0.25

Combine like terms: + 0.25 = 1.25

1.25 + x2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75

1.25 + x2 = 2.75

Factor a perfect square on the left side:

(x + 0.5) (x + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting

(x + 0.5) equal to 1.658312395 and - 1.658312395.

Subproblem 1

x + 0.5 = 1.658312395

Simplifying

x + 0.5 = 1.658312395

Reorder the terms:

0.5 + x = 1.658312395

Solving

0.5 + x = 1.658312395

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.

0.5 + - 0.5 + x = 1.658312395 + - 0.5

Combine like terms: 0.5 + - 0.5 = 0.0

0.0 + x = 1.658312395 + - 0.5

x = 1.658312395 + - 0.5

Combine like terms: 1.658312395 + - 0.5 = 1.158312395

x = 1.158312395

Simplifying

x = 1.158312395

Subproblem 2

x + 0.5 = - 1.658312395

Simplifying

x + 0.5 = - 1.658312395

Reorder the terms:

0.5 + x = - 1.658312395

Solving

0.5 + x = - 1.658312395

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.

0.5 + - 0.5 + x = - 1.658312395 + - 0.5

Combine like terms: 0.5 + - 0.5 = 0.0

0.0 + x = - 1.658312395 + - 0.5

x = - 1.658312395 + - 0.5

Combine like terms: - 1.658312395 + - 0.5 = - 2.158312395

x = - 2.158312395

Simplifying

x = - 2.158312395

Solution

The solution to the problem is based on the solutions

from the subproblems.

x = {1.158312395, - 2.158312395}