.8x^2+3.2x+2.40=0

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Solution for .8x^2+3.2x+2.40=0 equation:


Simplifying
0.8x2 + 3.2x + 2.40 = 0

Reorder the terms:
2.40 + 3.2x + 0.8x2 = 0

Solving
2.40 + 3.2x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
3 + 4x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 4x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 4x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x + x2 = 0 + -3
4x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4x + x2 = -3

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 = -3 + 4

Reorder the terms:
4 + 4x + x2 = -3 + 4

Combine like terms: -3 + 4 = 1
4 + 4x + x2 = 1

Factor a perfect square on the left side:
(x + 2)(x + 2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 2) equal to 1 and -1.

Subproblem 1

x + 2 = 1 Simplifying x + 2 = 1 Reorder the terms: 2 + x = 1 Solving 2 + x = 1 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 = 1 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1 + -2 x = 1 + -2 Combine like terms: 1 + -2 = -1 x = -1 Simplifying x = -1

Subproblem 2

x + 2 = -1 Simplifying x + 2 = -1 Reorder the terms: 2 + x = -1 Solving 2 + x = -1 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 = -1 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1 + -2 x = -1 + -2 Combine like terms: -1 + -2 = -3 x = -3 Simplifying x = -3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1, -3}

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