x^2+6.4x+10.24=0

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Solution for x^2+6.4x+10.24=0 equation:


Simplifying
x2 + 6.4x + 10.24 = 0

Reorder the terms:
10.24 + 6.4x + x2 = 0

Solving
10.24 + 6.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10.24' to each side of the equation.
10.24 + 6.4x + -10.24 + x2 = 0 + -10.24

Reorder the terms:
10.24 + -10.24 + 6.4x + x2 = 0 + -10.24

Combine like terms: 10.24 + -10.24 = 0.00
0.00 + 6.4x + x2 = 0 + -10.24
6.4x + x2 = 0 + -10.24

Combine like terms: 0 + -10.24 = -10.24
6.4x + x2 = -10.24

The x term is 6.4x.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4x + 10.24 + x2 = -10.24 + 10.24

Reorder the terms:
10.24 + 6.4x + x2 = -10.24 + 10.24

Combine like terms: -10.24 + 10.24 = 0.00
10.24 + 6.4x + x2 = 0.00

Factor a perfect square on the left side:
(x + 3.2)(x + 3.2) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 3.2) equal to 0.00 and 0.00.

Subproblem 1

x + 3.2 = 0.00 Simplifying x + 3.2 = 0.00 Reorder the terms: 3.2 + x = 0.00 Solving 3.2 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 0.00 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 0.00 + -3.2 x = 0.00 + -3.2 Combine like terms: 0.00 + -3.2 = -3.2 x = -3.2 Simplifying x = -3.2

Subproblem 2

x + 3.2 = 0.00 Simplifying x + 3.2 = 0.00 Reorder the terms: 3.2 + x = 0.00 Solving 3.2 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 0.00 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 0.00 + -3.2 x = 0.00 + -3.2 Combine like terms: 0.00 + -3.2 = -3.2 x = -3.2 Simplifying x = -3.2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.2, -3.2}

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