2x^2+30x+25=0

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Solution for 2x^2+30x+25=0 equation:


Simplifying
2x2 + 30x + 25 = 0

Reorder the terms:
25 + 30x + 2x2 = 0

Solving
25 + 30x + 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'.
12.5 + 15x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + 15x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + 15x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + 15x + x2 = 0 + -12.5
15x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
15x + x2 = -12.5

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -12.5 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -12.5 + 56.25

Combine like terms: -12.5 + 56.25 = 43.75
56.25 + 15x + x2 = 43.75

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.614378278 and -6.614378278.

Subproblem 1

x + 7.5 = 6.614378278 Simplifying x + 7.5 = 6.614378278 Reorder the terms: 7.5 + x = 6.614378278 Solving 7.5 + x = 6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.614378278 + -7.5 x = 6.614378278 + -7.5 Combine like terms: 6.614378278 + -7.5 = -0.885621722 x = -0.885621722 Simplifying x = -0.885621722

Subproblem 2

x + 7.5 = -6.614378278 Simplifying x + 7.5 = -6.614378278 Reorder the terms: 7.5 + x = -6.614378278 Solving 7.5 + x = -6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.614378278 + -7.5 x = -6.614378278 + -7.5 Combine like terms: -6.614378278 + -7.5 = -14.114378278 x = -14.114378278 Simplifying x = -14.114378278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.885621722, -14.114378278}

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