-4.9x^2+3.5x+11=0

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Solution for -4.9x^2+3.5x+11=0 equation:


Simplifying
-4.9x2 + 3.5x + 11 = 0

Reorder the terms:
11 + 3.5x + -4.9x2 = 0

Solving
11 + 3.5x + -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'.
-2.244897959 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '2.244897959' to each side of the equation.
-2.244897959 + -0.7142857143x + 2.244897959 + x2 = 0 + 2.244897959

Reorder the terms:
-2.244897959 + 2.244897959 + -0.7142857143x + x2 = 0 + 2.244897959

Combine like terms: -2.244897959 + 2.244897959 = 0.000000000
0.000000000 + -0.7142857143x + x2 = 0 + 2.244897959
-0.7142857143x + x2 = 0 + 2.244897959

Combine like terms: 0 + 2.244897959 = 2.244897959
-0.7142857143x + x2 = 2.244897959

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = 2.244897959 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = 2.244897959 + 0.1275510204

Combine like terms: 2.244897959 + 0.1275510204 = 2.3724489794
0.1275510204 + -0.7142857143x + x2 = 2.3724489794

Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = 2.3724489794

Calculate the square root of the right side: 1.540275618

Break this problem into two subproblems by setting 
(x + -0.3571428572) equal to 1.540275618 and -1.540275618.

Subproblem 1

x + -0.3571428572 = 1.540275618 Simplifying x + -0.3571428572 = 1.540275618 Reorder the terms: -0.3571428572 + x = 1.540275618 Solving -0.3571428572 + x = 1.540275618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.540275618 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.540275618 + 0.3571428572 x = 1.540275618 + 0.3571428572 Combine like terms: 1.540275618 + 0.3571428572 = 1.8974184752 x = 1.8974184752 Simplifying x = 1.8974184752

Subproblem 2

x + -0.3571428572 = -1.540275618 Simplifying x + -0.3571428572 = -1.540275618 Reorder the terms: -0.3571428572 + x = -1.540275618 Solving -0.3571428572 + x = -1.540275618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.540275618 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.540275618 + 0.3571428572 x = -1.540275618 + 0.3571428572 Combine like terms: -1.540275618 + 0.3571428572 = -1.1831327608 x = -1.1831327608 Simplifying x = -1.1831327608

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8974184752, -1.1831327608}

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