4.9x^2-34.64x+50=0

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Solution for 4.9x^2-34.64x+50=0 equation:


Simplifying
4.9x2 + -34.64x + 50 = 0

Reorder the terms:
50 + -34.64x + 4.9x2 = 0

Solving
50 + -34.64x + 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'.
10.20408163 + -7.069387755x + x2 = 0

Move the constant term to the right:

Add '-10.20408163' to each side of the equation.
10.20408163 + -7.069387755x + -10.20408163 + x2 = 0 + -10.20408163

Reorder the terms:
10.20408163 + -10.20408163 + -7.069387755x + x2 = 0 + -10.20408163

Combine like terms: 10.20408163 + -10.20408163 = 0.00000000
0.00000000 + -7.069387755x + x2 = 0 + -10.20408163
-7.069387755x + x2 = 0 + -10.20408163

Combine like terms: 0 + -10.20408163 = -10.20408163
-7.069387755x + x2 = -10.20408163

The x term is -7.069387755x.  Take half its coefficient (-3.534693878).
Square it (12.49406081) and add it to both sides.

Add '12.49406081' to each side of the equation.
-7.069387755x + 12.49406081 + x2 = -10.20408163 + 12.49406081

Reorder the terms:
12.49406081 + -7.069387755x + x2 = -10.20408163 + 12.49406081

Combine like terms: -10.20408163 + 12.49406081 = 2.28997918
12.49406081 + -7.069387755x + x2 = 2.28997918

Factor a perfect square on the left side:
(x + -3.534693878)(x + -3.534693878) = 2.28997918

Calculate the square root of the right side: 1.513267716

Break this problem into two subproblems by setting 
(x + -3.534693878) equal to 1.513267716 and -1.513267716.

Subproblem 1

x + -3.534693878 = 1.513267716 Simplifying x + -3.534693878 = 1.513267716 Reorder the terms: -3.534693878 + x = 1.513267716 Solving -3.534693878 + x = 1.513267716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.534693878' to each side of the equation. -3.534693878 + 3.534693878 + x = 1.513267716 + 3.534693878 Combine like terms: -3.534693878 + 3.534693878 = 0.000000000 0.000000000 + x = 1.513267716 + 3.534693878 x = 1.513267716 + 3.534693878 Combine like terms: 1.513267716 + 3.534693878 = 5.047961594 x = 5.047961594 Simplifying x = 5.047961594

Subproblem 2

x + -3.534693878 = -1.513267716 Simplifying x + -3.534693878 = -1.513267716 Reorder the terms: -3.534693878 + x = -1.513267716 Solving -3.534693878 + x = -1.513267716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.534693878' to each side of the equation. -3.534693878 + 3.534693878 + x = -1.513267716 + 3.534693878 Combine like terms: -3.534693878 + 3.534693878 = 0.000000000 0.000000000 + x = -1.513267716 + 3.534693878 x = -1.513267716 + 3.534693878 Combine like terms: -1.513267716 + 3.534693878 = 2.021426162 x = 2.021426162 Simplifying x = 2.021426162

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.047961594, 2.021426162}

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