3x^2+6x=25

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Solution for 3x^2+6x=25 equation:


Simplifying
3x2 + 6x = 25

Reorder the terms:
6x + 3x2 = 25

Solving
6x + 3x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 6x + 3x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 6x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 2x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 2x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 8.333333333
2x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
2x + x2 = 8.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 8.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 8.333333333 + 1

Combine like terms: 8.333333333 + 1 = 9.333333333
1 + 2x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + 1) equal to 3.055050463 and -3.055050463.

Subproblem 1

x + 1 = 3.055050463 Simplifying x + 1 = 3.055050463 Reorder the terms: 1 + x = 3.055050463 Solving 1 + x = 3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.055050463 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.055050463 + -1 x = 3.055050463 + -1 Combine like terms: 3.055050463 + -1 = 2.055050463 x = 2.055050463 Simplifying x = 2.055050463

Subproblem 2

x + 1 = -3.055050463 Simplifying x + 1 = -3.055050463 Reorder the terms: 1 + x = -3.055050463 Solving 1 + x = -3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.055050463 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.055050463 + -1 x = -3.055050463 + -1 Combine like terms: -3.055050463 + -1 = -4.055050463 x = -4.055050463 Simplifying x = -4.055050463

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.055050463, -4.055050463}

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