-7x(-4x-7)=4

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Solution for -7x(-4x-7)=4 equation:


Simplifying
-7x(-4x + -7) = 4

Reorder the terms:
-7x(-7 + -4x) = 4
(-7 * -7x + -4x * -7x) = 4
(49x + 28x2) = 4

Solving
49x + 28x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 49x + 28x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 49x + 28x2 = 0

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

Divide each side by '28'.
-0.1428571429 + 1.75x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 1.75x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 1.75x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 1.75x + x2 = 0 + 0.1428571429
1.75x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
1.75x + x2 = 0.1428571429

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 0.1428571429 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 0.1428571429 + 0.765625

Combine like terms: 0.1428571429 + 0.765625 = 0.9084821429
0.765625 + 1.75x + x2 = 0.9084821429

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 0.9084821429

Calculate the square root of the right side: 0.953143296

Break this problem into two subproblems by setting 
(x + 0.875) equal to 0.953143296 and -0.953143296.

Subproblem 1

x + 0.875 = 0.953143296 Simplifying x + 0.875 = 0.953143296 Reorder the terms: 0.875 + x = 0.953143296 Solving 0.875 + x = 0.953143296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 0.953143296 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 0.953143296 + -0.875 x = 0.953143296 + -0.875 Combine like terms: 0.953143296 + -0.875 = 0.078143296 x = 0.078143296 Simplifying x = 0.078143296

Subproblem 2

x + 0.875 = -0.953143296 Simplifying x + 0.875 = -0.953143296 Reorder the terms: 0.875 + x = -0.953143296 Solving 0.875 + x = -0.953143296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -0.953143296 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -0.953143296 + -0.875 x = -0.953143296 + -0.875 Combine like terms: -0.953143296 + -0.875 = -1.828143296 x = -1.828143296 Simplifying x = -1.828143296

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.078143296, -1.828143296}

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