5x*x+10x=-4

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Solution for 5x*x+10x=-4 equation:


Simplifying
5x * x + 10x = -4

Multiply x * x
5x2 + 10x = -4

Reorder the terms:
10x + 5x2 = -4

Solving
10x + 5x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 10x + 5x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 10x + 5x2 = 0

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

Divide each side by '5'.
0.8 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 2x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 2x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 2x + x2 = 0 + -0.8
2x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
2x + x2 = -0.8

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.8 + 1

Reorder the terms:
1 + 2x + x2 = -0.8 + 1

Combine like terms: -0.8 + 1 = 0.2
1 + 2x + x2 = 0.2

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + 1) equal to 0.447213596 and -0.447213596.

Subproblem 1

x + 1 = 0.447213596 Simplifying x + 1 = 0.447213596 Reorder the terms: 1 + x = 0.447213596 Solving 1 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.447213596 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.447213596 + -1 x = 0.447213596 + -1 Combine like terms: 0.447213596 + -1 = -0.552786404 x = -0.552786404 Simplifying x = -0.552786404

Subproblem 2

x + 1 = -0.447213596 Simplifying x + 1 = -0.447213596 Reorder the terms: 1 + x = -0.447213596 Solving 1 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.447213596 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.447213596 + -1 x = -0.447213596 + -1 Combine like terms: -0.447213596 + -1 = -1.447213596 x = -1.447213596 Simplifying x = -1.447213596

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.552786404, -1.447213596}

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