3x-(4x(5x-(6x-7)))=11

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Solution for 3x-(4x(5x-(6x-7)))=11 equation:


Simplifying
3x + -1(4x(5x + -1(6x + -7))) = 11

Reorder the terms:
3x + -1(4x(5x + -1(-7 + 6x))) = 11
3x + -1(4x(5x + (-7 * -1 + 6x * -1))) = 11
3x + -1(4x(5x + (7 + -6x))) = 11

Reorder the terms:
3x + -1(4x(7 + 5x + -6x)) = 11

Combine like terms: 5x + -6x = -1x
3x + -1(4x(7 + -1x)) = 11
3x + -1((7 * 4x + -1x * 4x)) = 11
3x + -1((28x + -4x2)) = 11
3x + (28x * -1 + -4x2 * -1) = 11
3x + (-28x + 4x2) = 11

Combine like terms: 3x + -28x = -25x
-25x + 4x2 = 11

Solving
-25x + 4x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + -25x + 4x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -25x + 4x2 = 0

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

Divide each side by '4'.
-2.75 + -6.25x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -6.25x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -6.25x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -6.25x + x2 = 0 + 2.75
-6.25x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-6.25x + x2 = 2.75

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 2.75 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 2.75 + 9.765625

Combine like terms: 2.75 + 9.765625 = 12.515625
9.765625 + -6.25x + x2 = 12.515625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 12.515625

Calculate the square root of the right side: 3.537742925

Break this problem into two subproblems by setting 
(x + -3.125) equal to 3.537742925 and -3.537742925.

Subproblem 1

x + -3.125 = 3.537742925 Simplifying x + -3.125 = 3.537742925 Reorder the terms: -3.125 + x = 3.537742925 Solving -3.125 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.537742925 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.537742925 + 3.125 x = 3.537742925 + 3.125 Combine like terms: 3.537742925 + 3.125 = 6.662742925 x = 6.662742925 Simplifying x = 6.662742925

Subproblem 2

x + -3.125 = -3.537742925 Simplifying x + -3.125 = -3.537742925 Reorder the terms: -3.125 + x = -3.537742925 Solving -3.125 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.537742925 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.537742925 + 3.125 x = -3.537742925 + 3.125 Combine like terms: -3.537742925 + 3.125 = -0.412742925 x = -0.412742925 Simplifying x = -0.412742925

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.662742925, -0.412742925}

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