5(x+9)+6x(5+x)=49

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Solution for 5(x+9)+6x(5+x)=49 equation:


Simplifying
5(x + 9) + 6x(5 + x) = 49

Reorder the terms:
5(9 + x) + 6x(5 + x) = 49
(9 * 5 + x * 5) + 6x(5 + x) = 49
(45 + 5x) + 6x(5 + x) = 49
45 + 5x + (5 * 6x + x * 6x) = 49
45 + 5x + (30x + 6x2) = 49

Combine like terms: 5x + 30x = 35x
45 + 35x + 6x2 = 49

Solving
45 + 35x + 6x2 = 49

Solving for variable 'x'.

Reorder the terms:
45 + -49 + 35x + 6x2 = 49 + -49

Combine like terms: 45 + -49 = -4
-4 + 35x + 6x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-4 + 35x + 6x2 = 0

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

Divide each side by '6'.
-0.6666666667 + 5.833333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 5.833333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 5.833333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 5.833333333x + x2 = 0 + 0.6666666667
5.833333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
5.833333333x + x2 = 0.6666666667

The x term is 5.833333333x.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333x + 8.506944446 + x2 = 0.6666666667 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333x + x2 = 0.6666666667 + 8.506944446

Combine like terms: 0.6666666667 + 8.506944446 = 9.1736111127
8.506944446 + 5.833333333x + x2 = 9.1736111127

Factor a perfect square on the left side:
(x + 2.916666667)(x + 2.916666667) = 9.1736111127

Calculate the square root of the right side: 3.028796974

Break this problem into two subproblems by setting 
(x + 2.916666667) equal to 3.028796974 and -3.028796974.

Subproblem 1

x + 2.916666667 = 3.028796974 Simplifying x + 2.916666667 = 3.028796974 Reorder the terms: 2.916666667 + x = 3.028796974 Solving 2.916666667 + x = 3.028796974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = 3.028796974 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = 3.028796974 + -2.916666667 x = 3.028796974 + -2.916666667 Combine like terms: 3.028796974 + -2.916666667 = 0.112130307 x = 0.112130307 Simplifying x = 0.112130307

Subproblem 2

x + 2.916666667 = -3.028796974 Simplifying x + 2.916666667 = -3.028796974 Reorder the terms: 2.916666667 + x = -3.028796974 Solving 2.916666667 + x = -3.028796974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = -3.028796974 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = -3.028796974 + -2.916666667 x = -3.028796974 + -2.916666667 Combine like terms: -3.028796974 + -2.916666667 = -5.945463641 x = -5.945463641 Simplifying x = -5.945463641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.112130307, -5.945463641}

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