-65=14x-.5-4.9(x^2)

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Solution for -65=14x-.5-4.9(x^2) equation:


Simplifying
-65 = 14x + -0.5 + -4.9(x2)

Reorder the terms:
-65 = -0.5 + 14x + -4.9x2

Solving
-65 = -0.5 + 14x + -4.9x2

Solving for variable 'x'.

Combine like terms: -65 + 0.5 = -64.5
-64.5 + -14x + 4.9x2 = -0.5 + 14x + -4.9x2 + 0.5 + -14x + 4.9x2

Reorder the terms:
-64.5 + -14x + 4.9x2 = -0.5 + 0.5 + 14x + -14x + -4.9x2 + 4.9x2

Combine like terms: -0.5 + 0.5 = 0.0
-64.5 + -14x + 4.9x2 = 0.0 + 14x + -14x + -4.9x2 + 4.9x2
-64.5 + -14x + 4.9x2 = 14x + -14x + -4.9x2 + 4.9x2

Combine like terms: 14x + -14x = 0
-64.5 + -14x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-64.5 + -14x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-64.5 + -14x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
-13.16326531 + -2.857142857x + x2 = 0

Move the constant term to the right:

Add '13.16326531' to each side of the equation.
-13.16326531 + -2.857142857x + 13.16326531 + x2 = 0 + 13.16326531

Reorder the terms:
-13.16326531 + 13.16326531 + -2.857142857x + x2 = 0 + 13.16326531

Combine like terms: -13.16326531 + 13.16326531 = 0.00000000
0.00000000 + -2.857142857x + x2 = 0 + 13.16326531
-2.857142857x + x2 = 0 + 13.16326531

Combine like terms: 0 + 13.16326531 = 13.16326531
-2.857142857x + x2 = 13.16326531

The x term is -2.857142857x.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857x + 2.040816328 + x2 = 13.16326531 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857x + x2 = 13.16326531 + 2.040816328

Combine like terms: 13.16326531 + 2.040816328 = 15.204081638
2.040816328 + -2.857142857x + x2 = 15.204081638

Factor a perfect square on the left side:
(x + -1.428571429)(x + -1.428571429) = 15.204081638

Calculate the square root of the right side: 3.899241162

Break this problem into two subproblems by setting 
(x + -1.428571429) equal to 3.899241162 and -3.899241162.

Subproblem 1

x + -1.428571429 = 3.899241162 Simplifying x + -1.428571429 = 3.899241162 Reorder the terms: -1.428571429 + x = 3.899241162 Solving -1.428571429 + x = 3.899241162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 3.899241162 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 3.899241162 + 1.428571429 x = 3.899241162 + 1.428571429 Combine like terms: 3.899241162 + 1.428571429 = 5.327812591 x = 5.327812591 Simplifying x = 5.327812591

Subproblem 2

x + -1.428571429 = -3.899241162 Simplifying x + -1.428571429 = -3.899241162 Reorder the terms: -1.428571429 + x = -3.899241162 Solving -1.428571429 + x = -3.899241162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -3.899241162 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -3.899241162 + 1.428571429 x = -3.899241162 + 1.428571429 Combine like terms: -3.899241162 + 1.428571429 = -2.470669733 x = -2.470669733 Simplifying x = -2.470669733

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.327812591, -2.470669733}

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