.05x^2+2x+2=

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Solution for .05x^2+2x+2= equation:


Simplifying
0.05x2 + 2x + 2 = 0

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

Solving
2 + 2x + 0.05x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.05'.
40 + 40x + x2 = 0

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 40x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 40x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 40x + x2 = 0 + -40
40x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
40x + x2 = -40

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -40 + 400

Reorder the terms:
400 + 40x + x2 = -40 + 400

Combine like terms: -40 + 400 = 360
400 + 40x + x2 = 360

Factor a perfect square on the left side:
(x + 20)(x + 20) = 360

Calculate the square root of the right side: 18.973665961

Break this problem into two subproblems by setting 
(x + 20) equal to 18.973665961 and -18.973665961.

Subproblem 1

x + 20 = 18.973665961 Simplifying x + 20 = 18.973665961 Reorder the terms: 20 + x = 18.973665961 Solving 20 + x = 18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 18.973665961 + -20 Combine like terms: 20 + -20 = 0 0 + x = 18.973665961 + -20 x = 18.973665961 + -20 Combine like terms: 18.973665961 + -20 = -1.026334039 x = -1.026334039 Simplifying x = -1.026334039

Subproblem 2

x + 20 = -18.973665961 Simplifying x + 20 = -18.973665961 Reorder the terms: 20 + x = -18.973665961 Solving 20 + x = -18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -18.973665961 + -20 Combine like terms: 20 + -20 = 0 0 + x = -18.973665961 + -20 x = -18.973665961 + -20 Combine like terms: -18.973665961 + -20 = -38.973665961 x = -38.973665961 Simplifying x = -38.973665961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.026334039, -38.973665961}

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