.4x^2+4x+7=0

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Solution for .4x^2+4x+7=0 equation:


Simplifying
0.4x2 + 4x + 7 = 0

Reorder the terms:
7 + 4x + 0.4x2 = 0

Solving
7 + 4x + 0.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.4'.
17.5 + 10x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + 10x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + 10x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + 10x + x2 = 0 + -17.5
10x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
10x + x2 = -17.5

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 = -17.5 + 25

Reorder the terms:
25 + 10x + x2 = -17.5 + 25

Combine like terms: -17.5 + 25 = 7.5
25 + 10x + x2 = 7.5

Factor a perfect square on the left side:
(x + 5)(x + 5) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(x + 5) equal to 2.738612788 and -2.738612788.

Subproblem 1

x + 5 = 2.738612788 Simplifying x + 5 = 2.738612788 Reorder the terms: 5 + x = 2.738612788 Solving 5 + x = 2.738612788 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 = 2.738612788 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.738612788 + -5 x = 2.738612788 + -5 Combine like terms: 2.738612788 + -5 = -2.261387212 x = -2.261387212 Simplifying x = -2.261387212

Subproblem 2

x + 5 = -2.738612788 Simplifying x + 5 = -2.738612788 Reorder the terms: 5 + x = -2.738612788 Solving 5 + x = -2.738612788 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 = -2.738612788 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.738612788 + -5 x = -2.738612788 + -5 Combine like terms: -2.738612788 + -5 = -7.738612788 x = -7.738612788 Simplifying x = -7.738612788

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.261387212, -7.738612788}

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