5x^2+25x=4x^2+56

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Solution for 5x^2+25x=4x^2+56 equation:


Simplifying
5x2 + 25x = 4x2 + 56

Reorder the terms:
25x + 5x2 = 4x2 + 56

Reorder the terms:
25x + 5x2 = 56 + 4x2

Solving
25x + 5x2 = 56 + 4x2

Solving for variable 'x'.

Reorder the terms:
-56 + 25x + 5x2 + -4x2 = 56 + 4x2 + -56 + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-56 + 25x + 1x2 = 56 + 4x2 + -56 + -4x2

Reorder the terms:
-56 + 25x + 1x2 = 56 + -56 + 4x2 + -4x2

Combine like terms: 56 + -56 = 0
-56 + 25x + 1x2 = 0 + 4x2 + -4x2
-56 + 25x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-56 + 25x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 25x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + 25x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 25x + x2 = 0 + 56
25x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
25x + x2 = 56

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 56 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 56 + 156.25

Combine like terms: 56 + 156.25 = 212.25
156.25 + 25x + x2 = 212.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 212.25

Calculate the square root of the right side: 14.568802284

Break this problem into two subproblems by setting 
(x + 12.5) equal to 14.568802284 and -14.568802284.

Subproblem 1

x + 12.5 = 14.568802284 Simplifying x + 12.5 = 14.568802284 Reorder the terms: 12.5 + x = 14.568802284 Solving 12.5 + x = 14.568802284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 14.568802284 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 14.568802284 + -12.5 x = 14.568802284 + -12.5 Combine like terms: 14.568802284 + -12.5 = 2.068802284 x = 2.068802284 Simplifying x = 2.068802284

Subproblem 2

x + 12.5 = -14.568802284 Simplifying x + 12.5 = -14.568802284 Reorder the terms: 12.5 + x = -14.568802284 Solving 12.5 + x = -14.568802284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -14.568802284 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -14.568802284 + -12.5 x = -14.568802284 + -12.5 Combine like terms: -14.568802284 + -12.5 = -27.068802284 x = -27.068802284 Simplifying x = -27.068802284

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.068802284, -27.068802284}

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