5(x+5)+6(3x+9)(7x+6)=

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Solution for 5(x+5)+6(3x+9)(7x+6)= equation:


Simplifying
5(x + 5) + 6(3x + 9)(7x + 6) = 0

Reorder the terms:
5(5 + x) + 6(3x + 9)(7x + 6) = 0
(5 * 5 + x * 5) + 6(3x + 9)(7x + 6) = 0
(25 + 5x) + 6(3x + 9)(7x + 6) = 0

Reorder the terms:
25 + 5x + 6(9 + 3x)(7x + 6) = 0

Reorder the terms:
25 + 5x + 6(9 + 3x)(6 + 7x) = 0

Multiply (9 + 3x) * (6 + 7x)
25 + 5x + 6(9(6 + 7x) + 3x * (6 + 7x)) = 0
25 + 5x + 6((6 * 9 + 7x * 9) + 3x * (6 + 7x)) = 0
25 + 5x + 6((54 + 63x) + 3x * (6 + 7x)) = 0
25 + 5x + 6(54 + 63x + (6 * 3x + 7x * 3x)) = 0
25 + 5x + 6(54 + 63x + (18x + 21x2)) = 0

Combine like terms: 63x + 18x = 81x
25 + 5x + 6(54 + 81x + 21x2) = 0
25 + 5x + (54 * 6 + 81x * 6 + 21x2 * 6) = 0
25 + 5x + (324 + 486x + 126x2) = 0

Reorder the terms:
25 + 324 + 5x + 486x + 126x2 = 0

Combine like terms: 25 + 324 = 349
349 + 5x + 486x + 126x2 = 0

Combine like terms: 5x + 486x = 491x
349 + 491x + 126x2 = 0

Solving
349 + 491x + 126x2 = 0

Solving for variable 'x'.

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

Divide each side by '126'.
2.76984127 + 3.896825397x + x2 = 0

Move the constant term to the right:

Add '-2.76984127' to each side of the equation.
2.76984127 + 3.896825397x + -2.76984127 + x2 = 0 + -2.76984127

Reorder the terms:
2.76984127 + -2.76984127 + 3.896825397x + x2 = 0 + -2.76984127

Combine like terms: 2.76984127 + -2.76984127 = 0.00000000
0.00000000 + 3.896825397x + x2 = 0 + -2.76984127
3.896825397x + x2 = 0 + -2.76984127

Combine like terms: 0 + -2.76984127 = -2.76984127
3.896825397x + x2 = -2.76984127

The x term is 3.896825397x.  Take half its coefficient (1.948412699).
Square it (3.796312046) and add it to both sides.

Add '3.796312046' to each side of the equation.
3.896825397x + 3.796312046 + x2 = -2.76984127 + 3.796312046

Reorder the terms:
3.796312046 + 3.896825397x + x2 = -2.76984127 + 3.796312046

Combine like terms: -2.76984127 + 3.796312046 = 1.026470776
3.796312046 + 3.896825397x + x2 = 1.026470776

Factor a perfect square on the left side:
(x + 1.948412699)(x + 1.948412699) = 1.026470776

Calculate the square root of the right side: 1.013148941

Break this problem into two subproblems by setting 
(x + 1.948412699) equal to 1.013148941 and -1.013148941.

Subproblem 1

x + 1.948412699 = 1.013148941 Simplifying x + 1.948412699 = 1.013148941 Reorder the terms: 1.948412699 + x = 1.013148941 Solving 1.948412699 + x = 1.013148941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.948412699' to each side of the equation. 1.948412699 + -1.948412699 + x = 1.013148941 + -1.948412699 Combine like terms: 1.948412699 + -1.948412699 = 0.000000000 0.000000000 + x = 1.013148941 + -1.948412699 x = 1.013148941 + -1.948412699 Combine like terms: 1.013148941 + -1.948412699 = -0.935263758 x = -0.935263758 Simplifying x = -0.935263758

Subproblem 2

x + 1.948412699 = -1.013148941 Simplifying x + 1.948412699 = -1.013148941 Reorder the terms: 1.948412699 + x = -1.013148941 Solving 1.948412699 + x = -1.013148941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.948412699' to each side of the equation. 1.948412699 + -1.948412699 + x = -1.013148941 + -1.948412699 Combine like terms: 1.948412699 + -1.948412699 = 0.000000000 0.000000000 + x = -1.013148941 + -1.948412699 x = -1.013148941 + -1.948412699 Combine like terms: -1.013148941 + -1.948412699 = -2.96156164 x = -2.96156164 Simplifying x = -2.96156164

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.935263758, -2.96156164}

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