-7x^2+16x-6=0

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Solution for -7x^2+16x-6=0 equation:


Simplifying
-7x2 + 16x + -6 = 0

Reorder the terms:
-6 + 16x + -7x2 = 0

Solving
-6 + 16x + -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'.
0.8571428571 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -2.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -2.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -2.285714286x + x2 = 0 + -0.8571428571
-2.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-2.285714286x + x2 = -0.8571428571

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = -0.8571428571 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = -0.8571428571 + 1.306122449

Combine like terms: -0.8571428571 + 1.306122449 = 0.4489795919
1.306122449 + -2.285714286x + x2 = 0.4489795919

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 0.4489795919

Calculate the square root of the right side: 0.670059394

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 0.670059394 and -0.670059394.

Subproblem 1

x + -1.142857143 = 0.670059394 Simplifying x + -1.142857143 = 0.670059394 Reorder the terms: -1.142857143 + x = 0.670059394 Solving -1.142857143 + x = 0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 0.670059394 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 0.670059394 + 1.142857143 x = 0.670059394 + 1.142857143 Combine like terms: 0.670059394 + 1.142857143 = 1.812916537 x = 1.812916537 Simplifying x = 1.812916537

Subproblem 2

x + -1.142857143 = -0.670059394 Simplifying x + -1.142857143 = -0.670059394 Reorder the terms: -1.142857143 + x = -0.670059394 Solving -1.142857143 + x = -0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -0.670059394 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -0.670059394 + 1.142857143 x = -0.670059394 + 1.142857143 Combine like terms: -0.670059394 + 1.142857143 = 0.472797749 x = 0.472797749 Simplifying x = 0.472797749

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.812916537, 0.472797749}

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