-7x^2-6x+2=0

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Solution for -7x^2-6x+2=0 equation:


Simplifying
-7x2 + -6x + 2 = 0

Reorder the terms:
2 + -6x + -7x2 = 0

Solving
2 + -6x + -7x2 = 0

Solving for variable 'x'.

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

Divide each side by '-7'.
-0.2857142857 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.8571428571x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 0.8571428571x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 0.8571428571x + x2 = 0 + 0.2857142857
0.8571428571x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
0.8571428571x + x2 = 0.2857142857

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 = 0.2857142857 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 0.2857142857 + 0.1836734694

Combine like terms: 0.2857142857 + 0.1836734694 = 0.4693877551
0.1836734694 + 0.8571428571x + x2 = 0.4693877551

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 0.4693877551

Calculate the square root of the right side: 0.685118789

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 0.685118789 and -0.685118789.

Subproblem 1

x + 0.4285714286 = 0.685118789 Simplifying x + 0.4285714286 = 0.685118789 Reorder the terms: 0.4285714286 + x = 0.685118789 Solving 0.4285714286 + x = 0.685118789 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 = 0.685118789 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.685118789 + -0.4285714286 x = 0.685118789 + -0.4285714286 Combine like terms: 0.685118789 + -0.4285714286 = 0.2565473604 x = 0.2565473604 Simplifying x = 0.2565473604

Subproblem 2

x + 0.4285714286 = -0.685118789 Simplifying x + 0.4285714286 = -0.685118789 Reorder the terms: 0.4285714286 + x = -0.685118789 Solving 0.4285714286 + x = -0.685118789 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 = -0.685118789 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.685118789 + -0.4285714286 x = -0.685118789 + -0.4285714286 Combine like terms: -0.685118789 + -0.4285714286 = -1.1136902176 x = -1.1136902176 Simplifying x = -1.1136902176

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2565473604, -1.1136902176}

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