4.946x^2=31.717x-3.361

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Solution for 4.946x^2=31.717x-3.361 equation:


Simplifying
4.946x2 = 31.717x + -3.361

Reorder the terms:
4.946x2 = -3.361 + 31.717x

Solving
4.946x2 = -3.361 + 31.717x

Solving for variable 'x'.

Reorder the terms:
3.361 + -31.717x + 4.946x2 = -3.361 + 31.717x + 3.361 + -31.717x

Reorder the terms:
3.361 + -31.717x + 4.946x2 = -3.361 + 3.361 + 31.717x + -31.717x

Combine like terms: -3.361 + 3.361 = 0.000
3.361 + -31.717x + 4.946x2 = 0.000 + 31.717x + -31.717x
3.361 + -31.717x + 4.946x2 = 31.717x + -31.717x

Combine like terms: 31.717x + -31.717x = 0.000
3.361 + -31.717x + 4.946x2 = 0.000

Begin completing the square.  Divide all terms by
4.946 the coefficient of the squared term: 

Divide each side by '4.946'.
0.6795390214 + -6.412656692x + x2 = 0

Move the constant term to the right:

Add '-0.6795390214' to each side of the equation.
0.6795390214 + -6.412656692x + -0.6795390214 + x2 = 0 + -0.6795390214

Reorder the terms:
0.6795390214 + -0.6795390214 + -6.412656692x + x2 = 0 + -0.6795390214

Combine like terms: 0.6795390214 + -0.6795390214 = 0.0000000000
0.0000000000 + -6.412656692x + x2 = 0 + -0.6795390214
-6.412656692x + x2 = 0 + -0.6795390214

Combine like terms: 0 + -0.6795390214 = -0.6795390214
-6.412656692x + x2 = -0.6795390214

The x term is -6.412656692x.  Take half its coefficient (-3.206328346).
Square it (10.28054146) and add it to both sides.

Add '10.28054146' to each side of the equation.
-6.412656692x + 10.28054146 + x2 = -0.6795390214 + 10.28054146

Reorder the terms:
10.28054146 + -6.412656692x + x2 = -0.6795390214 + 10.28054146

Combine like terms: -0.6795390214 + 10.28054146 = 9.6010024386
10.28054146 + -6.412656692x + x2 = 9.6010024386

Factor a perfect square on the left side:
(x + -3.206328346)(x + -3.206328346) = 9.6010024386

Calculate the square root of the right side: 3.098548441

Break this problem into two subproblems by setting 
(x + -3.206328346) equal to 3.098548441 and -3.098548441.

Subproblem 1

x + -3.206328346 = 3.098548441 Simplifying x + -3.206328346 = 3.098548441 Reorder the terms: -3.206328346 + x = 3.098548441 Solving -3.206328346 + x = 3.098548441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.206328346' to each side of the equation. -3.206328346 + 3.206328346 + x = 3.098548441 + 3.206328346 Combine like terms: -3.206328346 + 3.206328346 = 0.000000000 0.000000000 + x = 3.098548441 + 3.206328346 x = 3.098548441 + 3.206328346 Combine like terms: 3.098548441 + 3.206328346 = 6.304876787 x = 6.304876787 Simplifying x = 6.304876787

Subproblem 2

x + -3.206328346 = -3.098548441 Simplifying x + -3.206328346 = -3.098548441 Reorder the terms: -3.206328346 + x = -3.098548441 Solving -3.206328346 + x = -3.098548441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.206328346' to each side of the equation. -3.206328346 + 3.206328346 + x = -3.098548441 + 3.206328346 Combine like terms: -3.206328346 + 3.206328346 = 0.000000000 0.000000000 + x = -3.098548441 + 3.206328346 x = -3.098548441 + 3.206328346 Combine like terms: -3.098548441 + 3.206328346 = 0.107779905 x = 0.107779905 Simplifying x = 0.107779905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.304876787, 0.107779905}

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