25x^2=-96-184x

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Solution for 25x^2=-96-184x equation:


Simplifying
25x2 = -96 + -184x

Solving
25x2 = -96 + -184x

Solving for variable 'x'.

Reorder the terms:
96 + 184x + 25x2 = -96 + -184x + 96 + 184x

Reorder the terms:
96 + 184x + 25x2 = -96 + 96 + -184x + 184x

Combine like terms: -96 + 96 = 0
96 + 184x + 25x2 = 0 + -184x + 184x
96 + 184x + 25x2 = -184x + 184x

Combine like terms: -184x + 184x = 0
96 + 184x + 25x2 = 0

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

Divide each side by '25'.
3.84 + 7.36x + x2 = 0

Move the constant term to the right:

Add '-3.84' to each side of the equation.
3.84 + 7.36x + -3.84 + x2 = 0 + -3.84

Reorder the terms:
3.84 + -3.84 + 7.36x + x2 = 0 + -3.84

Combine like terms: 3.84 + -3.84 = 0.00
0.00 + 7.36x + x2 = 0 + -3.84
7.36x + x2 = 0 + -3.84

Combine like terms: 0 + -3.84 = -3.84
7.36x + x2 = -3.84

The x term is 7.36x.  Take half its coefficient (3.68).
Square it (13.5424) and add it to both sides.

Add '13.5424' to each side of the equation.
7.36x + 13.5424 + x2 = -3.84 + 13.5424

Reorder the terms:
13.5424 + 7.36x + x2 = -3.84 + 13.5424

Combine like terms: -3.84 + 13.5424 = 9.7024
13.5424 + 7.36x + x2 = 9.7024

Factor a perfect square on the left side:
(x + 3.68)(x + 3.68) = 9.7024

Calculate the square root of the right side: 3.114867573

Break this problem into two subproblems by setting 
(x + 3.68) equal to 3.114867573 and -3.114867573.

Subproblem 1

x + 3.68 = 3.114867573 Simplifying x + 3.68 = 3.114867573 Reorder the terms: 3.68 + x = 3.114867573 Solving 3.68 + x = 3.114867573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.68' to each side of the equation. 3.68 + -3.68 + x = 3.114867573 + -3.68 Combine like terms: 3.68 + -3.68 = 0.00 0.00 + x = 3.114867573 + -3.68 x = 3.114867573 + -3.68 Combine like terms: 3.114867573 + -3.68 = -0.565132427 x = -0.565132427 Simplifying x = -0.565132427

Subproblem 2

x + 3.68 = -3.114867573 Simplifying x + 3.68 = -3.114867573 Reorder the terms: 3.68 + x = -3.114867573 Solving 3.68 + x = -3.114867573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.68' to each side of the equation. 3.68 + -3.68 + x = -3.114867573 + -3.68 Combine like terms: 3.68 + -3.68 = 0.00 0.00 + x = -3.114867573 + -3.68 x = -3.114867573 + -3.68 Combine like terms: -3.114867573 + -3.68 = -6.794867573 x = -6.794867573 Simplifying x = -6.794867573

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.565132427, -6.794867573}

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