4.9x^2+49.05x-57.37=0

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Solution for 4.9x^2+49.05x-57.37=0 equation:


Simplifying
4.9x2 + 49.05x + -57.37 = 0

Reorder the terms:
-57.37 + 49.05x + 4.9x2 = 0

Solving
-57.37 + 49.05x + 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'.
-11.70816327 + 10.01020408x + x2 = 0

Move the constant term to the right:

Add '11.70816327' to each side of the equation.
-11.70816327 + 10.01020408x + 11.70816327 + x2 = 0 + 11.70816327

Reorder the terms:
-11.70816327 + 11.70816327 + 10.01020408x + x2 = 0 + 11.70816327

Combine like terms: -11.70816327 + 11.70816327 = 0.00000000
0.00000000 + 10.01020408x + x2 = 0 + 11.70816327
10.01020408x + x2 = 0 + 11.70816327

Combine like terms: 0 + 11.70816327 = 11.70816327
10.01020408x + x2 = 11.70816327

The x term is 10.01020408x.  Take half its coefficient (5.00510204).
Square it (25.05104643) and add it to both sides.

Add '25.05104643' to each side of the equation.
10.01020408x + 25.05104643 + x2 = 11.70816327 + 25.05104643

Reorder the terms:
25.05104643 + 10.01020408x + x2 = 11.70816327 + 25.05104643

Combine like terms: 11.70816327 + 25.05104643 = 36.7592097
25.05104643 + 10.01020408x + x2 = 36.7592097

Factor a perfect square on the left side:
(x + 5.00510204)(x + 5.00510204) = 36.7592097

Calculate the square root of the right side: 6.062937382

Break this problem into two subproblems by setting 
(x + 5.00510204) equal to 6.062937382 and -6.062937382.

Subproblem 1

x + 5.00510204 = 6.062937382 Simplifying x + 5.00510204 = 6.062937382 Reorder the terms: 5.00510204 + x = 6.062937382 Solving 5.00510204 + x = 6.062937382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.00510204' to each side of the equation. 5.00510204 + -5.00510204 + x = 6.062937382 + -5.00510204 Combine like terms: 5.00510204 + -5.00510204 = 0.00000000 0.00000000 + x = 6.062937382 + -5.00510204 x = 6.062937382 + -5.00510204 Combine like terms: 6.062937382 + -5.00510204 = 1.057835342 x = 1.057835342 Simplifying x = 1.057835342

Subproblem 2

x + 5.00510204 = -6.062937382 Simplifying x + 5.00510204 = -6.062937382 Reorder the terms: 5.00510204 + x = -6.062937382 Solving 5.00510204 + x = -6.062937382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.00510204' to each side of the equation. 5.00510204 + -5.00510204 + x = -6.062937382 + -5.00510204 Combine like terms: 5.00510204 + -5.00510204 = 0.00000000 0.00000000 + x = -6.062937382 + -5.00510204 x = -6.062937382 + -5.00510204 Combine like terms: -6.062937382 + -5.00510204 = -11.068039422 x = -11.068039422 Simplifying x = -11.068039422

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.057835342, -11.068039422}

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