10x^2+30x+21=0

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Solution for 10x^2+30x+21=0 equation:


Simplifying
10x2 + 30x + 21 = 0

Reorder the terms:
21 + 30x + 10x2 = 0

Solving
21 + 30x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
2.1 + 3x + x2 = 0

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + 3x + -2.1 + x2 = 0 + -2.1

Reorder the terms:
2.1 + -2.1 + 3x + x2 = 0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + 3x + x2 = 0 + -2.1
3x + x2 = 0 + -2.1

Combine like terms: 0 + -2.1 = -2.1
3x + x2 = -2.1

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -2.1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -2.1 + 2.25

Combine like terms: -2.1 + 2.25 = 0.15
2.25 + 3x + x2 = 0.15

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.387298335 and -0.387298335.

Subproblem 1

x + 1.5 = 0.387298335 Simplifying x + 1.5 = 0.387298335 Reorder the terms: 1.5 + x = 0.387298335 Solving 1.5 + x = 0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.387298335 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.387298335 + -1.5 x = 0.387298335 + -1.5 Combine like terms: 0.387298335 + -1.5 = -1.112701665 x = -1.112701665 Simplifying x = -1.112701665

Subproblem 2

x + 1.5 = -0.387298335 Simplifying x + 1.5 = -0.387298335 Reorder the terms: 1.5 + x = -0.387298335 Solving 1.5 + x = -0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.387298335 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.387298335 + -1.5 x = -0.387298335 + -1.5 Combine like terms: -0.387298335 + -1.5 = -1.887298335 x = -1.887298335 Simplifying x = -1.887298335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.112701665, -1.887298335}

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