0.1x^2-x-2.5=0

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Solution for 0.1x^2-x-2.5=0 equation:


Simplifying
0.1x2 + -1x + -2.5 = 0

Reorder the terms:
-2.5 + -1x + 0.1x2 = 0

Solving
-2.5 + -1x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
-25 + -10x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -10x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -10x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -10x + x2 = 0 + 25
-10x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-10x + x2 = 25

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 25 + 25

Reorder the terms:
25 + -10x + x2 = 25 + 25

Combine like terms: 25 + 25 = 50
25 + -10x + x2 = 50

Factor a perfect square on the left side:
(x + -5)(x + -5) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + -5) equal to 7.071067812 and -7.071067812.

Subproblem 1

x + -5 = 7.071067812 Simplifying x + -5 = 7.071067812 Reorder the terms: -5 + x = 7.071067812 Solving -5 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.071067812 + 5 x = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 x = 12.071067812 Simplifying x = 12.071067812

Subproblem 2

x + -5 = -7.071067812 Simplifying x + -5 = -7.071067812 Reorder the terms: -5 + x = -7.071067812 Solving -5 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.071067812 + 5 x = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 x = -2.071067812 Simplifying x = -2.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.071067812, -2.071067812}

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