1+1.3x+0.4x^2=0

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Solution for 1+1.3x+0.4x^2=0 equation:


Simplifying
1 + 1.3x + 0.4x2 = 0

Solving
1 + 1.3x + 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'.
2.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 3.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 3.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 3.25x + x2 = 0 + -2.5
3.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
3.25x + x2 = -2.5

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = -2.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = -2.5 + 2.640625

Combine like terms: -2.5 + 2.640625 = 0.140625
2.640625 + 3.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + 1.625) equal to 0.375 and -0.375.

Subproblem 1

x + 1.625 = 0.375 Simplifying x + 1.625 = 0.375 Reorder the terms: 1.625 + x = 0.375 Solving 1.625 + x = 0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 0.375 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 0.375 + -1.625 x = 0.375 + -1.625 Combine like terms: 0.375 + -1.625 = -1.25 x = -1.25 Simplifying x = -1.25

Subproblem 2

x + 1.625 = -0.375 Simplifying x + 1.625 = -0.375 Reorder the terms: 1.625 + x = -0.375 Solving 1.625 + x = -0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -0.375 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -0.375 + -1.625 x = -0.375 + -1.625 Combine like terms: -0.375 + -1.625 = -2 x = -2 Simplifying x = -2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.25, -2}

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