4.9x^2+18x-30=0

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Solution for 4.9x^2+18x-30=0 equation:


Simplifying
4.9x2 + 18x + -30 = 0

Reorder the terms:
-30 + 18x + 4.9x2 = 0

Solving
-30 + 18x + 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 + 3.673469388x + x2 = 0

Move the constant term to the right:

Add '6.12244898' to each side of the equation.
-6.12244898 + 3.673469388x + 6.12244898 + x2 = 0 + 6.12244898

Reorder the terms:
-6.12244898 + 6.12244898 + 3.673469388x + x2 = 0 + 6.12244898

Combine like terms: -6.12244898 + 6.12244898 = 0.00000000
0.00000000 + 3.673469388x + x2 = 0 + 6.12244898
3.673469388x + x2 = 0 + 6.12244898

Combine like terms: 0 + 6.12244898 = 6.12244898
3.673469388x + x2 = 6.12244898

The x term is 3.673469388x.  Take half its coefficient (1.836734694).
Square it (3.373594336) and add it to both sides.

Add '3.373594336' to each side of the equation.
3.673469388x + 3.373594336 + x2 = 6.12244898 + 3.373594336

Reorder the terms:
3.373594336 + 3.673469388x + x2 = 6.12244898 + 3.373594336

Combine like terms: 6.12244898 + 3.373594336 = 9.496043316
3.373594336 + 3.673469388x + x2 = 9.496043316

Factor a perfect square on the left side:
(x + 1.836734694)(x + 1.836734694) = 9.496043316

Calculate the square root of the right side: 3.081565076

Break this problem into two subproblems by setting 
(x + 1.836734694) equal to 3.081565076 and -3.081565076.


Subproblem 1
x + 1.836734694 = 3.081565076

Simplifying
x + 1.836734694 = 3.081565076

Reorder the terms:
1.836734694 + x = 3.081565076

Solving
1.836734694 + x = 3.081565076

Solving for variable 'x'.

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

Add '-1.836734694' to each side of the equation.
1.836734694 + -1.836734694 + x = 3.081565076 + -1.836734694

Combine like terms: 1.836734694 + -1.836734694 = 0.000000000
0.000000000 + x = 3.081565076 + -1.836734694
x = 3.081565076 + -1.836734694

Combine like terms: 3.081565076 + -1.836734694 = 1.244830382
x = 1.244830382

Simplifying
x = 1.244830382


Subproblem 2
x + 1.836734694 = -3.081565076

Simplifying
x + 1.836734694 = -3.081565076

Reorder the terms:
1.836734694 + x = -3.081565076

Solving
1.836734694 + x = -3.081565076

Solving for variable 'x'.

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

Add '-1.836734694' to each side of the equation.
1.836734694 + -1.836734694 + x = -3.081565076 + -1.836734694

Combine like terms: 1.836734694 + -1.836734694 = 0.000000000
0.000000000 + x = -3.081565076 + -1.836734694
x = -3.081565076 + -1.836734694

Combine like terms: -3.081565076 + -1.836734694 = -4.91829977
x = -4.91829977

Simplifying
x = -4.91829977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.244830382, -4.91829977}

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