2x^2+24x+5=0

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Solution for 2x^2+24x+5=0 equation:


Simplifying
2x2 + 24x + 5 = 0

Reorder the terms:
5 + 24x + 2x2 = 0

Solving
5 + 24x + 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'.
2.5 + 12x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 12x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 12x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 12x + x2 = 0 + -2.5
12x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
12x + x2 = -2.5

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -2.5 + 36

Reorder the terms:
36 + 12x + x2 = -2.5 + 36

Combine like terms: -2.5 + 36 = 33.5
36 + 12x + x2 = 33.5

Factor a perfect square on the left side:
(x + 6)(x + 6) = 33.5

Calculate the square root of the right side: 5.787918451

Break this problem into two subproblems by setting 
(x + 6) equal to 5.787918451 and -5.787918451.

Subproblem 1

x + 6 = 5.787918451 Simplifying x + 6 = 5.787918451 Reorder the terms: 6 + x = 5.787918451 Solving 6 + x = 5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.787918451 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.787918451 + -6 x = 5.787918451 + -6 Combine like terms: 5.787918451 + -6 = -0.212081549 x = -0.212081549 Simplifying x = -0.212081549

Subproblem 2

x + 6 = -5.787918451 Simplifying x + 6 = -5.787918451 Reorder the terms: 6 + x = -5.787918451 Solving 6 + x = -5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.787918451 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.787918451 + -6 x = -5.787918451 + -6 Combine like terms: -5.787918451 + -6 = -11.787918451 x = -11.787918451 Simplifying x = -11.787918451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.212081549, -11.787918451}

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