7x^2-11=-6x

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Solution for 7x^2-11=-6x equation:


Simplifying
7x2 + -11 = -6x

Reorder the terms:
-11 + 7x2 = -6x

Solving
-11 + 7x2 = -6x

Solving for variable 'x'.

Reorder the terms:
-11 + 6x + 7x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-11 + 6x + 7x2 = 0

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

Divide each side by '7'.
-1.571428571 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 0.8571428571x + 1.571428571 + x2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 0.8571428571x + x2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 0.8571428571x + x2 = 0 + 1.571428571
0.8571428571x + x2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
0.8571428571x + x2 = 1.571428571

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 1.571428571 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 1.571428571 + 0.1836734694

Combine like terms: 1.571428571 + 0.1836734694 = 1.7551020404
0.1836734694 + 0.8571428571x + x2 = 1.7551020404

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 1.7551020404

Calculate the square root of the right side: 1.324802642

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 1.324802642 and -1.324802642.

Subproblem 1

x + 0.4285714286 = 1.324802642 Simplifying x + 0.4285714286 = 1.324802642 Reorder the terms: 0.4285714286 + x = 1.324802642 Solving 0.4285714286 + x = 1.324802642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 1.324802642 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.324802642 + -0.4285714286 x = 1.324802642 + -0.4285714286 Combine like terms: 1.324802642 + -0.4285714286 = 0.8962312134 x = 0.8962312134 Simplifying x = 0.8962312134

Subproblem 2

x + 0.4285714286 = -1.324802642 Simplifying x + 0.4285714286 = -1.324802642 Reorder the terms: 0.4285714286 + x = -1.324802642 Solving 0.4285714286 + x = -1.324802642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -1.324802642 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.324802642 + -0.4285714286 x = -1.324802642 + -0.4285714286 Combine like terms: -1.324802642 + -0.4285714286 = -1.7533740706 x = -1.7533740706 Simplifying x = -1.7533740706

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8962312134, -1.7533740706}

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