5x+3x(7x-11)=149

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Solution for 5x+3x(7x-11)=149 equation:


Simplifying
5x + 3x(7x + -11) = 149

Reorder the terms:
5x + 3x(-11 + 7x) = 149
5x + (-11 * 3x + 7x * 3x) = 149
5x + (-33x + 21x2) = 149

Combine like terms: 5x + -33x = -28x
-28x + 21x2 = 149

Solving
-28x + 21x2 = 149

Solving for variable 'x'.

Reorder the terms:
-149 + -28x + 21x2 = 149 + -149

Combine like terms: 149 + -149 = 0
-149 + -28x + 21x2 = 0

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

Divide each side by '21'.
-7.095238095 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '7.095238095' to each side of the equation.
-7.095238095 + -1.333333333x + 7.095238095 + x2 = 0 + 7.095238095

Reorder the terms:
-7.095238095 + 7.095238095 + -1.333333333x + x2 = 0 + 7.095238095

Combine like terms: -7.095238095 + 7.095238095 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 7.095238095
-1.333333333x + x2 = 0 + 7.095238095

Combine like terms: 0 + 7.095238095 = 7.095238095
-1.333333333x + x2 = 7.095238095

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 7.095238095 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 7.095238095 + 0.4444444442

Combine like terms: 7.095238095 + 0.4444444442 = 7.5396825392
0.4444444442 + -1.333333333x + x2 = 7.5396825392

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 7.5396825392

Calculate the square root of the right side: 2.745848237

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.745848237 and -2.745848237.

Subproblem 1

x + -0.6666666665 = 2.745848237 Simplifying x + -0.6666666665 = 2.745848237 Reorder the terms: -0.6666666665 + x = 2.745848237 Solving -0.6666666665 + x = 2.745848237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.745848237 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.745848237 + 0.6666666665 x = 2.745848237 + 0.6666666665 Combine like terms: 2.745848237 + 0.6666666665 = 3.4125149035 x = 3.4125149035 Simplifying x = 3.4125149035

Subproblem 2

x + -0.6666666665 = -2.745848237 Simplifying x + -0.6666666665 = -2.745848237 Reorder the terms: -0.6666666665 + x = -2.745848237 Solving -0.6666666665 + x = -2.745848237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.745848237 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.745848237 + 0.6666666665 x = -2.745848237 + 0.6666666665 Combine like terms: -2.745848237 + 0.6666666665 = -2.0791815705 x = -2.0791815705 Simplifying x = -2.0791815705

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.4125149035, -2.0791815705}

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