1.57x+4.91x^2=2.00

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Solution for 1.57x+4.91x^2=2.00 equation:


Simplifying
1.57x + 4.91x2 = 2.00

Solving
1.57x + 4.91x2 = 2.00

Solving for variable 'x'.

Reorder the terms:
-2.00 + 1.57x + 4.91x2 = 2.00 + -2.00

Combine like terms: 2.00 + -2.00 = 0.00
-2.00 + 1.57x + 4.91x2 = 0.00

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

Divide each side by '4.91'.
-0.4073319756 + 0.3197556008x + x2 = 0

Move the constant term to the right:

Add '0.4073319756' to each side of the equation.
-0.4073319756 + 0.3197556008x + 0.4073319756 + x2 = 0 + 0.4073319756

Reorder the terms:
-0.4073319756 + 0.4073319756 + 0.3197556008x + x2 = 0 + 0.4073319756

Combine like terms: -0.4073319756 + 0.4073319756 = 0.0000000000
0.0000000000 + 0.3197556008x + x2 = 0 + 0.4073319756
0.3197556008x + x2 = 0 + 0.4073319756

Combine like terms: 0 + 0.4073319756 = 0.4073319756
0.3197556008x + x2 = 0.4073319756

The x term is 0.3197556008x.  Take half its coefficient (0.1598778004).
Square it (0.02556091106) and add it to both sides.

Add '0.02556091106' to each side of the equation.
0.3197556008x + 0.02556091106 + x2 = 0.4073319756 + 0.02556091106

Reorder the terms:
0.02556091106 + 0.3197556008x + x2 = 0.4073319756 + 0.02556091106

Combine like terms: 0.4073319756 + 0.02556091106 = 0.43289288666
0.02556091106 + 0.3197556008x + x2 = 0.43289288666

Factor a perfect square on the left side:
(x + 0.1598778004)(x + 0.1598778004) = 0.43289288666

Calculate the square root of the right side: 0.65794596

Break this problem into two subproblems by setting 
(x + 0.1598778004) equal to 0.65794596 and -0.65794596.

Subproblem 1

x + 0.1598778004 = 0.65794596 Simplifying x + 0.1598778004 = 0.65794596 Reorder the terms: 0.1598778004 + x = 0.65794596 Solving 0.1598778004 + x = 0.65794596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1598778004' to each side of the equation. 0.1598778004 + -0.1598778004 + x = 0.65794596 + -0.1598778004 Combine like terms: 0.1598778004 + -0.1598778004 = 0.0000000000 0.0000000000 + x = 0.65794596 + -0.1598778004 x = 0.65794596 + -0.1598778004 Combine like terms: 0.65794596 + -0.1598778004 = 0.4980681596 x = 0.4980681596 Simplifying x = 0.4980681596

Subproblem 2

x + 0.1598778004 = -0.65794596 Simplifying x + 0.1598778004 = -0.65794596 Reorder the terms: 0.1598778004 + x = -0.65794596 Solving 0.1598778004 + x = -0.65794596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1598778004' to each side of the equation. 0.1598778004 + -0.1598778004 + x = -0.65794596 + -0.1598778004 Combine like terms: 0.1598778004 + -0.1598778004 = 0.0000000000 0.0000000000 + x = -0.65794596 + -0.1598778004 x = -0.65794596 + -0.1598778004 Combine like terms: -0.65794596 + -0.1598778004 = -0.8178237604 x = -0.8178237604 Simplifying x = -0.8178237604

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4980681596, -0.8178237604}

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