20=42*x+4.9*x^2

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Solution for 20=42*x+4.9*x^2 equation:


Simplifying
20 = 42x + 4.9x2

Solving
20 = 42x + 4.9x2

Solving for variable 'x'.

Reorder the terms:
20 + -42x + -4.9x2 = 42x + -42x + 4.9x2 + -4.9x2

Combine like terms: 42x + -42x = 0
20 + -42x + -4.9x2 = 0 + 4.9x2 + -4.9x2
20 + -42x + -4.9x2 = 4.9x2 + -4.9x2

Combine like terms: 4.9x2 + -4.9x2 = 0.0
20 + -42x + -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'.
-4.081632653 + 8.571428571x + x2 = 0

Move the constant term to the right:

Add '4.081632653' to each side of the equation.
-4.081632653 + 8.571428571x + 4.081632653 + x2 = 0 + 4.081632653

Reorder the terms:
-4.081632653 + 4.081632653 + 8.571428571x + x2 = 0 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + 8.571428571x + x2 = 0 + 4.081632653
8.571428571x + x2 = 0 + 4.081632653

Combine like terms: 0 + 4.081632653 = 4.081632653
8.571428571x + x2 = 4.081632653

The x term is 8.571428571x.  Take half its coefficient (4.285714286).
Square it (18.36734694) and add it to both sides.

Add '18.36734694' to each side of the equation.
8.571428571x + 18.36734694 + x2 = 4.081632653 + 18.36734694

Reorder the terms:
18.36734694 + 8.571428571x + x2 = 4.081632653 + 18.36734694

Combine like terms: 4.081632653 + 18.36734694 = 22.448979593
18.36734694 + 8.571428571x + x2 = 22.448979593

Factor a perfect square on the left side:
(x + 4.285714286)(x + 4.285714286) = 22.448979593

Calculate the square root of the right side: 4.738035415

Break this problem into two subproblems by setting 
(x + 4.285714286) equal to 4.738035415 and -4.738035415.

Subproblem 1

x + 4.285714286 = 4.738035415 Simplifying x + 4.285714286 = 4.738035415 Reorder the terms: 4.285714286 + x = 4.738035415 Solving 4.285714286 + x = 4.738035415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + x = 4.738035415 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + x = 4.738035415 + -4.285714286 x = 4.738035415 + -4.285714286 Combine like terms: 4.738035415 + -4.285714286 = 0.452321129 x = 0.452321129 Simplifying x = 0.452321129

Subproblem 2

x + 4.285714286 = -4.738035415 Simplifying x + 4.285714286 = -4.738035415 Reorder the terms: 4.285714286 + x = -4.738035415 Solving 4.285714286 + x = -4.738035415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + x = -4.738035415 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + x = -4.738035415 + -4.285714286 x = -4.738035415 + -4.285714286 Combine like terms: -4.738035415 + -4.285714286 = -9.023749701 x = -9.023749701 Simplifying x = -9.023749701

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.452321129, -9.023749701}

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