2x+7x^2-4=0

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Solution for 2x+7x^2-4=0 equation:


Simplifying
2x + 7x2 + -4 = 0

Reorder the terms:
-4 + 2x + 7x2 = 0

Solving
-4 + 2x + 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'.
-0.5714285714 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 0.2857142857x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 0.2857142857x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 0.2857142857x + x2 = 0 + 0.5714285714
0.2857142857x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
0.2857142857x + x2 = 0.5714285714

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 = 0.5714285714 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 0.5714285714 + 0.02040816328

Combine like terms: 0.5714285714 + 0.02040816328 = 0.59183673468
0.02040816328 + 0.2857142857x + x2 = 0.59183673468

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 0.59183673468

Calculate the square root of the right side: 0.769309258

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 0.769309258 and -0.769309258.

Subproblem 1

x + 0.1428571429 = 0.769309258 Simplifying x + 0.1428571429 = 0.769309258 Reorder the terms: 0.1428571429 + x = 0.769309258 Solving 0.1428571429 + x = 0.769309258 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 = 0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.769309258 + -0.1428571429 x = 0.769309258 + -0.1428571429 Combine like terms: 0.769309258 + -0.1428571429 = 0.6264521151 x = 0.6264521151 Simplifying x = 0.6264521151

Subproblem 2

x + 0.1428571429 = -0.769309258 Simplifying x + 0.1428571429 = -0.769309258 Reorder the terms: 0.1428571429 + x = -0.769309258 Solving 0.1428571429 + x = -0.769309258 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 = -0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.769309258 + -0.1428571429 x = -0.769309258 + -0.1428571429 Combine like terms: -0.769309258 + -0.1428571429 = -0.9121664009 x = -0.9121664009 Simplifying x = -0.9121664009

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6264521151, -0.9121664009}

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