0.5x^2+2x-0.05=0

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Solution for 0.5x^2+2x-0.05=0 equation:


Simplifying
0.5x2 + 2x + -0.05 = 0

Reorder the terms:
-0.05 + 2x + 0.5x2 = 0

Solving
-0.05 + 2x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-0.1 + 4x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 4x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 4x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 4x + x2 = 0 + 0.1
4x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
4x + x2 = 0.1

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 = 0.1 + 4

Reorder the terms:
4 + 4x + x2 = 0.1 + 4

Combine like terms: 0.1 + 4 = 4.1
4 + 4x + x2 = 4.1

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.1

Calculate the square root of the right side: 2.024845673

Break this problem into two subproblems by setting 
(x + 2) equal to 2.024845673 and -2.024845673.

Subproblem 1

x + 2 = 2.024845673 Simplifying x + 2 = 2.024845673 Reorder the terms: 2 + x = 2.024845673 Solving 2 + x = 2.024845673 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 = 2.024845673 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.024845673 + -2 x = 2.024845673 + -2 Combine like terms: 2.024845673 + -2 = 0.024845673 x = 0.024845673 Simplifying x = 0.024845673

Subproblem 2

x + 2 = -2.024845673 Simplifying x + 2 = -2.024845673 Reorder the terms: 2 + x = -2.024845673 Solving 2 + x = -2.024845673 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 = -2.024845673 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.024845673 + -2 x = -2.024845673 + -2 Combine like terms: -2.024845673 + -2 = -4.024845673 x = -4.024845673 Simplifying x = -4.024845673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.024845673, -4.024845673}

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