2x^2+21x+30=0

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


Simplifying
2x2 + 21x + 30 = 0

Reorder the terms:
30 + 21x + 2x2 = 0

Solving
30 + 21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
15 + 10.5x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 10.5x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 10.5x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 10.5x + x2 = 0 + -15
10.5x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
10.5x + x2 = -15

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = -15 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = -15 + 27.5625

Combine like terms: -15 + 27.5625 = 12.5625
27.5625 + 10.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + 5.25) equal to 3.54436172 and -3.54436172.

Subproblem 1

x + 5.25 = 3.54436172 Simplifying x + 5.25 = 3.54436172 Reorder the terms: 5.25 + x = 3.54436172 Solving 5.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 3.54436172 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 3.54436172 + -5.25 x = 3.54436172 + -5.25 Combine like terms: 3.54436172 + -5.25 = -1.70563828 x = -1.70563828 Simplifying x = -1.70563828

Subproblem 2

x + 5.25 = -3.54436172 Simplifying x + 5.25 = -3.54436172 Reorder the terms: 5.25 + x = -3.54436172 Solving 5.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -3.54436172 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -3.54436172 + -5.25 x = -3.54436172 + -5.25 Combine like terms: -3.54436172 + -5.25 = -8.79436172 x = -8.79436172 Simplifying x = -8.79436172

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.70563828, -8.79436172}

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