14x=-18+49x^2

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Solution for 14x=-18+49x^2 equation:


Simplifying
14x = -18 + 49x2

Solving
14x = -18 + 49x2

Solving for variable 'x'.

Reorder the terms:
18 + 14x + -49x2 = -18 + 49x2 + 18 + -49x2

Reorder the terms:
18 + 14x + -49x2 = -18 + 18 + 49x2 + -49x2

Combine like terms: -18 + 18 = 0
18 + 14x + -49x2 = 0 + 49x2 + -49x2
18 + 14x + -49x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
18 + 14x + -49x2 = 0

Begin completing the square.  Divide all terms by
-49 the coefficient of the squared term: 

Divide each side by '-49'.
-0.3673469388 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.3673469388' to each side of the equation.
-0.3673469388 + -0.2857142857x + 0.3673469388 + x2 = 0 + 0.3673469388

Reorder the terms:
-0.3673469388 + 0.3673469388 + -0.2857142857x + x2 = 0 + 0.3673469388

Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000
0.0000000000 + -0.2857142857x + x2 = 0 + 0.3673469388
-0.2857142857x + x2 = 0 + 0.3673469388

Combine like terms: 0 + 0.3673469388 = 0.3673469388
-0.2857142857x + x2 = 0.3673469388

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 = 0.3673469388 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 0.3673469388 + 0.02040816328

Combine like terms: 0.3673469388 + 0.02040816328 = 0.38775510208
0.02040816328 + -0.2857142857x + x2 = 0.38775510208

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 0.38775510208

Calculate the square root of the right side: 0.622699849

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 0.622699849 and -0.622699849.

Subproblem 1

x + -0.1428571429 = 0.622699849 Simplifying x + -0.1428571429 = 0.622699849 Reorder the terms: -0.1428571429 + x = 0.622699849 Solving -0.1428571429 + x = 0.622699849 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 = 0.622699849 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.622699849 + 0.1428571429 x = 0.622699849 + 0.1428571429 Combine like terms: 0.622699849 + 0.1428571429 = 0.7655569919 x = 0.7655569919 Simplifying x = 0.7655569919

Subproblem 2

x + -0.1428571429 = -0.622699849 Simplifying x + -0.1428571429 = -0.622699849 Reorder the terms: -0.1428571429 + x = -0.622699849 Solving -0.1428571429 + x = -0.622699849 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 = -0.622699849 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.622699849 + 0.1428571429 x = -0.622699849 + 0.1428571429 Combine like terms: -0.622699849 + 0.1428571429 = -0.4798427061 x = -0.4798427061 Simplifying x = -0.4798427061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7655569919, -0.4798427061}

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