6x(-7x+8)+7(x+1)=

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Solution for 6x(-7x+8)+7(x+1)= equation:


Simplifying
6x(-7x + 8) + 7(x + 1) = 0

Reorder the terms:
6x(8 + -7x) + 7(x + 1) = 0
(8 * 6x + -7x * 6x) + 7(x + 1) = 0
(48x + -42x2) + 7(x + 1) = 0

Reorder the terms:
48x + -42x2 + 7(1 + x) = 0
48x + -42x2 + (1 * 7 + x * 7) = 0
48x + -42x2 + (7 + 7x) = 0

Reorder the terms:
7 + 48x + 7x + -42x2 = 0

Combine like terms: 48x + 7x = 55x
7 + 55x + -42x2 = 0

Solving
7 + 55x + -42x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-42 the coefficient of the squared term: 

Divide each side by '-42'.
-0.1666666667 + -1.30952381x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -1.30952381x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -1.30952381x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -1.30952381x + x2 = 0 + 0.1666666667
-1.30952381x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-1.30952381x + x2 = 0.1666666667

The x term is -1.30952381x.  Take half its coefficient (-0.654761905).
Square it (0.4287131522) and add it to both sides.

Add '0.4287131522' to each side of the equation.
-1.30952381x + 0.4287131522 + x2 = 0.1666666667 + 0.4287131522

Reorder the terms:
0.4287131522 + -1.30952381x + x2 = 0.1666666667 + 0.4287131522

Combine like terms: 0.1666666667 + 0.4287131522 = 0.5953798189
0.4287131522 + -1.30952381x + x2 = 0.5953798189

Factor a perfect square on the left side:
(x + -0.654761905)(x + -0.654761905) = 0.5953798189

Calculate the square root of the right side: 0.771608592

Break this problem into two subproblems by setting 
(x + -0.654761905) equal to 0.771608592 and -0.771608592.

Subproblem 1

x + -0.654761905 = 0.771608592 Simplifying x + -0.654761905 = 0.771608592 Reorder the terms: -0.654761905 + x = 0.771608592 Solving -0.654761905 + x = 0.771608592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.654761905' to each side of the equation. -0.654761905 + 0.654761905 + x = 0.771608592 + 0.654761905 Combine like terms: -0.654761905 + 0.654761905 = 0.000000000 0.000000000 + x = 0.771608592 + 0.654761905 x = 0.771608592 + 0.654761905 Combine like terms: 0.771608592 + 0.654761905 = 1.426370497 x = 1.426370497 Simplifying x = 1.426370497

Subproblem 2

x + -0.654761905 = -0.771608592 Simplifying x + -0.654761905 = -0.771608592 Reorder the terms: -0.654761905 + x = -0.771608592 Solving -0.654761905 + x = -0.771608592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.654761905' to each side of the equation. -0.654761905 + 0.654761905 + x = -0.771608592 + 0.654761905 Combine like terms: -0.654761905 + 0.654761905 = 0.000000000 0.000000000 + x = -0.771608592 + 0.654761905 x = -0.771608592 + 0.654761905 Combine like terms: -0.771608592 + 0.654761905 = -0.116846687 x = -0.116846687 Simplifying x = -0.116846687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.426370497, -0.116846687}

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