7x^2-2x=3

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Solution for 7x^2-2x=3 equation:


Simplifying
7x2 + -2x = 3

Reorder the terms:
-2x + 7x2 = 3

Solving
-2x + 7x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -2x + 7x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -2x + 7x2 = 0

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

Divide each side by '7'.
-0.4285714286 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -0.2857142857x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -0.2857142857x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -0.2857142857x + x2 = 0 + 0.4285714286
-0.2857142857x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-0.2857142857x + x2 = 0.4285714286

The x term is -0.2857142857x.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857x + 0.02040816328 + x2 = 0.4285714286 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 0.4285714286 + 0.02040816328

Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188
0.02040816328 + -0.2857142857x + x2 = 0.44897959188

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 0.44897959188

Calculate the square root of the right side: 0.670059394

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 0.670059394 and -0.670059394.

Subproblem 1

x + -0.1428571429 = 0.670059394 Simplifying x + -0.1428571429 = 0.670059394 Reorder the terms: -0.1428571429 + x = 0.670059394 Solving -0.1428571429 + x = 0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.670059394 + 0.1428571429 x = 0.670059394 + 0.1428571429 Combine like terms: 0.670059394 + 0.1428571429 = 0.8129165369 x = 0.8129165369 Simplifying x = 0.8129165369

Subproblem 2

x + -0.1428571429 = -0.670059394 Simplifying x + -0.1428571429 = -0.670059394 Reorder the terms: -0.1428571429 + x = -0.670059394 Solving -0.1428571429 + x = -0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.670059394 + 0.1428571429 x = -0.670059394 + 0.1428571429 Combine like terms: -0.670059394 + 0.1428571429 = -0.5272022511 x = -0.5272022511 Simplifying x = -0.5272022511

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8129165369, -0.5272022511}

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