3x-0.5x^2=2.5

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Solution for 3x-0.5x^2=2.5 equation:


Simplifying
3x + -0.5x2 = 2.5

Solving
3x + -0.5x2 = 2.5

Solving for variable 'x'.

Reorder the terms:
-2.5 + 3x + -0.5x2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + 3x + -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'.
5 + -6x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -6x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -6x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x + x2 = 0 + -5
-6x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6x + x2 = -5

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -5 + 9

Reorder the terms:
9 + -6x + x2 = -5 + 9

Combine like terms: -5 + 9 = 4
9 + -6x + x2 = 4

Factor a perfect square on the left side:
(x + -3)(x + -3) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -3) equal to 2 and -2.

Subproblem 1

x + -3 = 2 Simplifying x + -3 = 2 Reorder the terms: -3 + x = 2 Solving -3 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2 + 3 x = 2 + 3 Combine like terms: 2 + 3 = 5 x = 5 Simplifying x = 5

Subproblem 2

x + -3 = -2 Simplifying x + -3 = -2 Reorder the terms: -3 + x = -2 Solving -3 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2 + 3 x = -2 + 3 Combine like terms: -2 + 3 = 1 x = 1 Simplifying x = 1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5, 1}

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