-4.9x^2+30x+1.4=0

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Solution for -4.9x^2+30x+1.4=0 equation: 


Simplifying
-4.9x2 + 30x + 1.4 = 0

Reorder the terms:
1.4 + 30x + -4.9x2 = 0

Solving
1.4 + 30x + -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'.
-0.2857142857 + -6.12244898x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -6.12244898x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -6.12244898x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -6.12244898x + x2 = 0 + 0.2857142857
-6.12244898x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-6.12244898x + x2 = 0.2857142857

The x term is -6.12244898x.  Take half its coefficient (-3.06122449).
Square it (9.371095378) and add it to both sides.

Add '9.371095378' to each side of the equation.
-6.12244898x + 9.371095378 + x2 = 0.2857142857 + 9.371095378

Reorder the terms:
9.371095378 + -6.12244898x + x2 = 0.2857142857 + 9.371095378

Combine like terms: 0.2857142857 + 9.371095378 = 9.6568096637
9.371095378 + -6.12244898x + x2 = 9.6568096637

Factor a perfect square on the left side:
(x + -3.06122449)(x + -3.06122449) = 9.6568096637

Calculate the square root of the right side: 3.107540774

Break this problem into two subproblems by setting 
(x + -3.06122449) equal to 3.107540774 and -3.107540774.


Subproblem 1
x + -3.06122449 = 3.107540774

Simplifying
x + -3.06122449 = 3.107540774

Reorder the terms:
-3.06122449 + x = 3.107540774

Solving
-3.06122449 + x = 3.107540774

Solving for variable 'x'.

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

Add '3.06122449' to each side of the equation.
-3.06122449 + 3.06122449 + x = 3.107540774 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + x = 3.107540774 + 3.06122449
x = 3.107540774 + 3.06122449

Combine like terms: 3.107540774 + 3.06122449 = 6.168765264
x = 6.168765264

Simplifying
x = 6.168765264


Subproblem 2
x + -3.06122449 = -3.107540774

Simplifying
x + -3.06122449 = -3.107540774

Reorder the terms:
-3.06122449 + x = -3.107540774

Solving
-3.06122449 + x = -3.107540774

Solving for variable 'x'.

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

Add '3.06122449' to each side of the equation.
-3.06122449 + 3.06122449 + x = -3.107540774 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + x = -3.107540774 + 3.06122449
x = -3.107540774 + 3.06122449

Combine like terms: -3.107540774 + 3.06122449 = -0.046316284
x = -0.046316284

Simplifying
x = -0.046316284


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.168765264, -0.046316284}

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