-2.75=-.5x^2+x

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Solution for -2.75=-.5x^2+x equation:


Simplifying
-2.75 = -0.5x2 + x

Reorder the terms:
-2.75 = x + -0.5x2

Solving
-2.75 = x + -0.5x2

Solving for variable 'x'.

Reorder the terms:
-2.75 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2

Combine like terms: x + -1x = 0
-2.75 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2
-2.75 + -1x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
-2.75 + -1x + 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'.
-5.5 + -2x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -2x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -2x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -2x + x2 = 0 + 5.5
-2x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-2x + x2 = 5.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 5.5 + 1

Reorder the terms:
1 + -2x + x2 = 5.5 + 1

Combine like terms: 5.5 + 1 = 6.5
1 + -2x + x2 = 6.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -1) equal to 2.549509757 and -2.549509757.

Subproblem 1

x + -1 = 2.549509757 Simplifying x + -1 = 2.549509757 Reorder the terms: -1 + x = 2.549509757 Solving -1 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.549509757 + 1 x = 2.549509757 + 1 Combine like terms: 2.549509757 + 1 = 3.549509757 x = 3.549509757 Simplifying x = 3.549509757

Subproblem 2

x + -1 = -2.549509757 Simplifying x + -1 = -2.549509757 Reorder the terms: -1 + x = -2.549509757 Solving -1 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.549509757 + 1 x = -2.549509757 + 1 Combine like terms: -2.549509757 + 1 = -1.549509757 x = -1.549509757 Simplifying x = -1.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.549509757, -1.549509757}

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