28x^2=-69-184x

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Solution for 28x^2=-69-184x equation:


Simplifying
28x2 = -69 + -184x

Solving
28x2 = -69 + -184x

Solving for variable 'x'.

Reorder the terms:
69 + 184x + 28x2 = -69 + -184x + 69 + 184x

Reorder the terms:
69 + 184x + 28x2 = -69 + 69 + -184x + 184x

Combine like terms: -69 + 69 = 0
69 + 184x + 28x2 = 0 + -184x + 184x
69 + 184x + 28x2 = -184x + 184x

Combine like terms: -184x + 184x = 0
69 + 184x + 28x2 = 0

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

Divide each side by '28'.
2.464285714 + 6.571428571x + x2 = 0

Move the constant term to the right:

Add '-2.464285714' to each side of the equation.
2.464285714 + 6.571428571x + -2.464285714 + x2 = 0 + -2.464285714

Reorder the terms:
2.464285714 + -2.464285714 + 6.571428571x + x2 = 0 + -2.464285714

Combine like terms: 2.464285714 + -2.464285714 = 0.000000000
0.000000000 + 6.571428571x + x2 = 0 + -2.464285714
6.571428571x + x2 = 0 + -2.464285714

Combine like terms: 0 + -2.464285714 = -2.464285714
6.571428571x + x2 = -2.464285714

The x term is 6.571428571x.  Take half its coefficient (3.285714286).
Square it (10.79591837) and add it to both sides.

Add '10.79591837' to each side of the equation.
6.571428571x + 10.79591837 + x2 = -2.464285714 + 10.79591837

Reorder the terms:
10.79591837 + 6.571428571x + x2 = -2.464285714 + 10.79591837

Combine like terms: -2.464285714 + 10.79591837 = 8.331632656
10.79591837 + 6.571428571x + x2 = 8.331632656

Factor a perfect square on the left side:
(x + 3.285714286)(x + 3.285714286) = 8.331632656

Calculate the square root of the right side: 2.886456765

Break this problem into two subproblems by setting 
(x + 3.285714286) equal to 2.886456765 and -2.886456765.

Subproblem 1

x + 3.285714286 = 2.886456765 Simplifying x + 3.285714286 = 2.886456765 Reorder the terms: 3.285714286 + x = 2.886456765 Solving 3.285714286 + x = 2.886456765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = 2.886456765 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = 2.886456765 + -3.285714286 x = 2.886456765 + -3.285714286 Combine like terms: 2.886456765 + -3.285714286 = -0.399257521 x = -0.399257521 Simplifying x = -0.399257521

Subproblem 2

x + 3.285714286 = -2.886456765 Simplifying x + 3.285714286 = -2.886456765 Reorder the terms: 3.285714286 + x = -2.886456765 Solving 3.285714286 + x = -2.886456765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = -2.886456765 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = -2.886456765 + -3.285714286 x = -2.886456765 + -3.285714286 Combine like terms: -2.886456765 + -3.285714286 = -6.172171051 x = -6.172171051 Simplifying x = -6.172171051

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.399257521, -6.172171051}

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