2x^2+15x+20=0

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Solution for 2x^2+15x+20=0 equation:


Simplifying
2x2 + 15x + 20 = 0

Reorder the terms:
20 + 15x + 2x2 = 0

Solving
20 + 15x + 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'.
10 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 7.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 7.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7.5x + x2 = 0 + -10
7.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
7.5x + x2 = -10

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -10 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -10 + 14.0625

Combine like terms: -10 + 14.0625 = 4.0625
14.0625 + 7.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 3.75) equal to 2.015564437 and -2.015564437.

Subproblem 1

x + 3.75 = 2.015564437 Simplifying x + 3.75 = 2.015564437 Reorder the terms: 3.75 + x = 2.015564437 Solving 3.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 2.015564437 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.015564437 + -3.75 x = 2.015564437 + -3.75 Combine like terms: 2.015564437 + -3.75 = -1.734435563 x = -1.734435563 Simplifying x = -1.734435563

Subproblem 2

x + 3.75 = -2.015564437 Simplifying x + 3.75 = -2.015564437 Reorder the terms: 3.75 + x = -2.015564437 Solving 3.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -2.015564437 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.015564437 + -3.75 x = -2.015564437 + -3.75 Combine like terms: -2.015564437 + -3.75 = -5.765564437 x = -5.765564437 Simplifying x = -5.765564437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.734435563, -5.765564437}

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