10x^2+48x+10=0

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Solution for 10x^2+48x+10=0 equation: 


Simplifying
10x2 + 48x + 10 = 0

Reorder the terms:
10 + 48x + 10x2 = 0

Solving
10 + 48x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 24x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 24x + 5x2)' equal to zero and attempt to solve:

Simplifying
5 + 24x + 5x2 = 0

Solving
5 + 24x + 5x2 = 0

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

Divide each side by '5'.
1 + 4.8x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.8x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4.8x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.8x + x2 = 0 + -1
4.8x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.8x + x2 = -1

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = -1 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = -1 + 5.76

Combine like terms: -1 + 5.76 = 4.76
5.76 + 4.8x + x2 = 4.76

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 4.76

Calculate the square root of the right side: 2.181742423

Break this problem into two subproblems by setting 
(x + 2.4) equal to 2.181742423 and -2.181742423.


Subproblem 1
x + 2.4 = 2.181742423

Simplifying
x + 2.4 = 2.181742423

Reorder the terms:
2.4 + x = 2.181742423

Solving
2.4 + x = 2.181742423

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 2.181742423 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 2.181742423 + -2.4
x = 2.181742423 + -2.4

Combine like terms: 2.181742423 + -2.4 = -0.218257577
x = -0.218257577

Simplifying
x = -0.218257577


Subproblem 2
x + 2.4 = -2.181742423

Simplifying
x + 2.4 = -2.181742423

Reorder the terms:
2.4 + x = -2.181742423

Solving
2.4 + x = -2.181742423

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -2.181742423 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -2.181742423 + -2.4
x = -2.181742423 + -2.4

Combine like terms: -2.181742423 + -2.4 = -4.581742423
x = -4.581742423

Simplifying
x = -4.581742423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.218257577, -4.581742423}
Solution
x = {-0.218257577, -4.581742423}

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