2.22x+4.91x^2=2.00

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Solution for 2.22x+4.91x^2=2.00 equation:


Simplifying
2.22x + 4.91x2 = 2.00

Solving
2.22x + 4.91x2 = 2.00

Solving for variable 'x'.

Reorder the terms:
-2.00 + 2.22x + 4.91x2 = 2.00 + -2.00

Combine like terms: 2.00 + -2.00 = 0.00
-2.00 + 2.22x + 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 + 0.4521384929x + x2 = 0

Move the constant term to the right:

Add '0.4073319756' to each side of the equation.
-0.4073319756 + 0.4521384929x + 0.4073319756 + x2 = 0 + 0.4073319756

Reorder the terms:
-0.4073319756 + 0.4073319756 + 0.4521384929x + x2 = 0 + 0.4073319756

Combine like terms: -0.4073319756 + 0.4073319756 = 0.0000000000
0.0000000000 + 0.4521384929x + x2 = 0 + 0.4073319756
0.4521384929x + x2 = 0 + 0.4073319756

Combine like terms: 0 + 0.4073319756 = 0.4073319756
0.4521384929x + x2 = 0.4073319756

The x term is 0.4521384929x.  Take half its coefficient (0.2260692465).
Square it (0.05110730421) and add it to both sides.

Add '0.05110730421' to each side of the equation.
0.4521384929x + 0.05110730421 + x2 = 0.4073319756 + 0.05110730421

Reorder the terms:
0.05110730421 + 0.4521384929x + x2 = 0.4073319756 + 0.05110730421

Combine like terms: 0.4073319756 + 0.05110730421 = 0.45843927981
0.05110730421 + 0.4521384929x + x2 = 0.45843927981

Factor a perfect square on the left side:
(x + 0.2260692465)(x + 0.2260692465) = 0.45843927981

Calculate the square root of the right side: 0.677081443

Break this problem into two subproblems by setting 
(x + 0.2260692465) equal to 0.677081443 and -0.677081443.

Subproblem 1

x + 0.2260692465 = 0.677081443 Simplifying x + 0.2260692465 = 0.677081443 Reorder the terms: 0.2260692465 + x = 0.677081443 Solving 0.2260692465 + x = 0.677081443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2260692465' to each side of the equation. 0.2260692465 + -0.2260692465 + x = 0.677081443 + -0.2260692465 Combine like terms: 0.2260692465 + -0.2260692465 = 0.0000000000 0.0000000000 + x = 0.677081443 + -0.2260692465 x = 0.677081443 + -0.2260692465 Combine like terms: 0.677081443 + -0.2260692465 = 0.4510121965 x = 0.4510121965 Simplifying x = 0.4510121965

Subproblem 2

x + 0.2260692465 = -0.677081443 Simplifying x + 0.2260692465 = -0.677081443 Reorder the terms: 0.2260692465 + x = -0.677081443 Solving 0.2260692465 + x = -0.677081443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2260692465' to each side of the equation. 0.2260692465 + -0.2260692465 + x = -0.677081443 + -0.2260692465 Combine like terms: 0.2260692465 + -0.2260692465 = 0.0000000000 0.0000000000 + x = -0.677081443 + -0.2260692465 x = -0.677081443 + -0.2260692465 Combine like terms: -0.677081443 + -0.2260692465 = -0.9031506895 x = -0.9031506895 Simplifying x = -0.9031506895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4510121965, -0.9031506895}

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