2x(2x+4x)-5=6x+9

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Solution for 2x(2x+4x)-5=6x+9 equation:


Simplifying
2x(2x + 4x) + -5 = 6x + 9

Combine like terms: 2x + 4x = 6x
2x(6x) + -5 = 6x + 9

Remove parenthesis around (6x)
2x * 6x + -5 = 6x + 9

Reorder the terms for easier multiplication:
2 * 6x * x + -5 = 6x + 9

Multiply 2 * 6
12x * x + -5 = 6x + 9

Multiply x * x
12x2 + -5 = 6x + 9

Reorder the terms:
-5 + 12x2 = 6x + 9

Reorder the terms:
-5 + 12x2 = 9 + 6x

Solving
-5 + 12x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
-5 + -9 + -6x + 12x2 = 9 + 6x + -9 + -6x

Combine like terms: -5 + -9 = -14
-14 + -6x + 12x2 = 9 + 6x + -9 + -6x

Reorder the terms:
-14 + -6x + 12x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
-14 + -6x + 12x2 = 0 + 6x + -6x
-14 + -6x + 12x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-14 + -6x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -3x + 6x2)' equal to zero and attempt to solve: Simplifying -7 + -3x + 6x2 = 0 Solving -7 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -0.5x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -0.5x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 1.166666667 -0.5x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -0.5x + x2 = 1.166666667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.166666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.166666667 + 0.0625 Combine like terms: 1.166666667 + 0.0625 = 1.229166667 0.0625 + -0.5x + x2 = 1.229166667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.229166667 Calculate the square root of the right side: 1.108677891 Break this problem into two subproblems by setting (x + -0.25) equal to 1.108677891 and -1.108677891.

Subproblem 1

x + -0.25 = 1.108677891 Simplifying x + -0.25 = 1.108677891 Reorder the terms: -0.25 + x = 1.108677891 Solving -0.25 + x = 1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.108677891 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.108677891 + 0.25 x = 1.108677891 + 0.25 Combine like terms: 1.108677891 + 0.25 = 1.358677891 x = 1.358677891 Simplifying x = 1.358677891

Subproblem 2

x + -0.25 = -1.108677891 Simplifying x + -0.25 = -1.108677891 Reorder the terms: -0.25 + x = -1.108677891 Solving -0.25 + x = -1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.108677891 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.108677891 + 0.25 x = -1.108677891 + 0.25 Combine like terms: -1.108677891 + 0.25 = -0.858677891 x = -0.858677891 Simplifying x = -0.858677891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.358677891, -0.858677891}

Solution

x = {1.358677891, -0.858677891}

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