4.9x^2+12x-30=0

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Solution for 4.9x^2+12x-30=0 equation: 


Simplifying
4.9x2 + 12x + -30 = 0

Reorder the terms:
-30 + 12x + 4.9x2 = 0

Solving
-30 + 12x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-6.12244898 + 2.448979592x + x2 = 0

Move the constant term to the right:

Add '6.12244898' to each side of the equation.
-6.12244898 + 2.448979592x + 6.12244898 + x2 = 0 + 6.12244898

Reorder the terms:
-6.12244898 + 6.12244898 + 2.448979592x + x2 = 0 + 6.12244898

Combine like terms: -6.12244898 + 6.12244898 = 0.00000000
0.00000000 + 2.448979592x + x2 = 0 + 6.12244898
2.448979592x + x2 = 0 + 6.12244898

Combine like terms: 0 + 6.12244898 = 6.12244898
2.448979592x + x2 = 6.12244898

The x term is 2.448979592x.  Take half its coefficient (1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
2.448979592x + 1.499375261 + x2 = 6.12244898 + 1.499375261

Reorder the terms:
1.499375261 + 2.448979592x + x2 = 6.12244898 + 1.499375261

Combine like terms: 6.12244898 + 1.499375261 = 7.621824241
1.499375261 + 2.448979592x + x2 = 7.621824241

Factor a perfect square on the left side:
(x + 1.224489796)(x + 1.224489796) = 7.621824241

Calculate the square root of the right side: 2.760765155

Break this problem into two subproblems by setting 
(x + 1.224489796) equal to 2.760765155 and -2.760765155.


Subproblem 1
x + 1.224489796 = 2.760765155

Simplifying
x + 1.224489796 = 2.760765155

Reorder the terms:
1.224489796 + x = 2.760765155

Solving
1.224489796 + x = 2.760765155

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.224489796' to each side of the equation.
1.224489796 + -1.224489796 + x = 2.760765155 + -1.224489796

Combine like terms: 1.224489796 + -1.224489796 = 0.000000000
0.000000000 + x = 2.760765155 + -1.224489796
x = 2.760765155 + -1.224489796

Combine like terms: 2.760765155 + -1.224489796 = 1.536275359
x = 1.536275359

Simplifying
x = 1.536275359


Subproblem 2
x + 1.224489796 = -2.760765155

Simplifying
x + 1.224489796 = -2.760765155

Reorder the terms:
1.224489796 + x = -2.760765155

Solving
1.224489796 + x = -2.760765155

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.224489796' to each side of the equation.
1.224489796 + -1.224489796 + x = -2.760765155 + -1.224489796

Combine like terms: 1.224489796 + -1.224489796 = 0.000000000
0.000000000 + x = -2.760765155 + -1.224489796
x = -2.760765155 + -1.224489796

Combine like terms: -2.760765155 + -1.224489796 = -3.985254951
x = -3.985254951

Simplifying
x = -3.985254951


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.536275359, -3.985254951}

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