3.86=12.3x-4.9x^2

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Solution for 3.86=12.3x-4.9x^2 equation:


Simplifying
3.86 = 12.3x + -4.9x2

Solving
3.86 = 12.3x + -4.9x2

Solving for variable 'x'.

Reorder the terms:
3.86 + -12.3x + 4.9x2 = 12.3x + -12.3x + -4.9x2 + 4.9x2

Combine like terms: 12.3x + -12.3x = 0.0
3.86 + -12.3x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
3.86 + -12.3x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
3.86 + -12.3x + 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'.
0.787755102 + -2.510204082x + x2 = 0

Move the constant term to the right:

Add '-0.787755102' to each side of the equation.
0.787755102 + -2.510204082x + -0.787755102 + x2 = 0 + -0.787755102

Reorder the terms:
0.787755102 + -0.787755102 + -2.510204082x + x2 = 0 + -0.787755102

Combine like terms: 0.787755102 + -0.787755102 = 0.000000000
0.000000000 + -2.510204082x + x2 = 0 + -0.787755102
-2.510204082x + x2 = 0 + -0.787755102

Combine like terms: 0 + -0.787755102 = -0.787755102
-2.510204082x + x2 = -0.787755102

The x term is -2.510204082x.  Take half its coefficient (-1.255102041).
Square it (1.575281133) and add it to both sides.

Add '1.575281133' to each side of the equation.
-2.510204082x + 1.575281133 + x2 = -0.787755102 + 1.575281133

Reorder the terms:
1.575281133 + -2.510204082x + x2 = -0.787755102 + 1.575281133

Combine like terms: -0.787755102 + 1.575281133 = 0.787526031
1.575281133 + -2.510204082x + x2 = 0.787526031

Factor a perfect square on the left side:
(x + -1.255102041)(x + -1.255102041) = 0.787526031

Calculate the square root of the right side: 0.887426634

Break this problem into two subproblems by setting 
(x + -1.255102041) equal to 0.887426634 and -0.887426634.

Subproblem 1

x + -1.255102041 = 0.887426634 Simplifying x + -1.255102041 = 0.887426634 Reorder the terms: -1.255102041 + x = 0.887426634 Solving -1.255102041 + x = 0.887426634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.255102041' to each side of the equation. -1.255102041 + 1.255102041 + x = 0.887426634 + 1.255102041 Combine like terms: -1.255102041 + 1.255102041 = 0.000000000 0.000000000 + x = 0.887426634 + 1.255102041 x = 0.887426634 + 1.255102041 Combine like terms: 0.887426634 + 1.255102041 = 2.142528675 x = 2.142528675 Simplifying x = 2.142528675

Subproblem 2

x + -1.255102041 = -0.887426634 Simplifying x + -1.255102041 = -0.887426634 Reorder the terms: -1.255102041 + x = -0.887426634 Solving -1.255102041 + x = -0.887426634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.255102041' to each side of the equation. -1.255102041 + 1.255102041 + x = -0.887426634 + 1.255102041 Combine like terms: -1.255102041 + 1.255102041 = 0.000000000 0.000000000 + x = -0.887426634 + 1.255102041 x = -0.887426634 + 1.255102041 Combine like terms: -0.887426634 + 1.255102041 = 0.367675407 x = 0.367675407 Simplifying x = 0.367675407

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.142528675, 0.367675407}

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