-2x+3=0.5x^2-5.5

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Solution for -2x+3=0.5x^2-5.5 equation:


Simplifying
-2x + 3 = 0.5x2 + -5.5

Reorder the terms:
3 + -2x = 0.5x2 + -5.5

Reorder the terms:
3 + -2x = -5.5 + 0.5x2

Solving
3 + -2x = -5.5 + 0.5x2

Solving for variable 'x'.

Reorder the terms:
3 + 5.5 + -2x + -0.5x2 = -5.5 + 0.5x2 + 5.5 + -0.5x2

Combine like terms: 3 + 5.5 = 8.5
8.5 + -2x + -0.5x2 = -5.5 + 0.5x2 + 5.5 + -0.5x2

Reorder the terms:
8.5 + -2x + -0.5x2 = -5.5 + 5.5 + 0.5x2 + -0.5x2

Combine like terms: -5.5 + 5.5 = 0.0
8.5 + -2x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
8.5 + -2x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
8.5 + -2x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-17 + 4x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 4x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 4x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 4x + x2 = 0 + 17
4x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
4x + x2 = 17

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 17 + 4

Reorder the terms:
4 + 4x + x2 = 17 + 4

Combine like terms: 17 + 4 = 21
4 + 4x + x2 = 21

Factor a perfect square on the left side:
(x + 2)(x + 2) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 2) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + 2 = 4.582575695 Simplifying x + 2 = 4.582575695 Reorder the terms: 2 + x = 4.582575695 Solving 2 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.582575695 + -2 x = 4.582575695 + -2 Combine like terms: 4.582575695 + -2 = 2.582575695 x = 2.582575695 Simplifying x = 2.582575695

Subproblem 2

x + 2 = -4.582575695 Simplifying x + 2 = -4.582575695 Reorder the terms: 2 + x = -4.582575695 Solving 2 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.582575695 + -2 x = -4.582575695 + -2 Combine like terms: -4.582575695 + -2 = -6.582575695 x = -6.582575695 Simplifying x = -6.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.582575695, -6.582575695}

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