2323x^2=909-90x

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Solution for 2323x^2=909-90x equation:


Simplifying
2323x2 = 909 + -90x

Solving
2323x2 = 909 + -90x

Solving for variable 'x'.

Reorder the terms:
-909 + 90x + 2323x2 = 909 + -90x + -909 + 90x

Reorder the terms:
-909 + 90x + 2323x2 = 909 + -909 + -90x + 90x

Combine like terms: 909 + -909 = 0
-909 + 90x + 2323x2 = 0 + -90x + 90x
-909 + 90x + 2323x2 = -90x + 90x

Combine like terms: -90x + 90x = 0
-909 + 90x + 2323x2 = 0

Begin completing the square.  Divide all terms by
2323 the coefficient of the squared term: 

Divide each side by '2323'.
-0.3913043478 + 0.03874300474x + x2 = 0

Move the constant term to the right:

Add '0.3913043478' to each side of the equation.
-0.3913043478 + 0.03874300474x + 0.3913043478 + x2 = 0 + 0.3913043478

Reorder the terms:
-0.3913043478 + 0.3913043478 + 0.03874300474x + x2 = 0 + 0.3913043478

Combine like terms: -0.3913043478 + 0.3913043478 = 0.0000000000
0.0000000000 + 0.03874300474x + x2 = 0 + 0.3913043478
0.03874300474x + x2 = 0 + 0.3913043478

Combine like terms: 0 + 0.3913043478 = 0.3913043478
0.03874300474x + x2 = 0.3913043478

The x term is 0.03874300474x.  Take half its coefficient (0.01937150237).
Square it (0.0003752551041) and add it to both sides.

Add '0.0003752551041' to each side of the equation.
0.03874300474x + 0.0003752551041 + x2 = 0.3913043478 + 0.0003752551041

Reorder the terms:
0.0003752551041 + 0.03874300474x + x2 = 0.3913043478 + 0.0003752551041

Combine like terms: 0.3913043478 + 0.0003752551041 = 0.3916796029041
0.0003752551041 + 0.03874300474x + x2 = 0.3916796029041

Factor a perfect square on the left side:
(x + 0.01937150237)(x + 0.01937150237) = 0.3916796029041

Calculate the square root of the right side: 0.625843114

Break this problem into two subproblems by setting 
(x + 0.01937150237) equal to 0.625843114 and -0.625843114.

Subproblem 1

x + 0.01937150237 = 0.625843114 Simplifying x + 0.01937150237 = 0.625843114 Reorder the terms: 0.01937150237 + x = 0.625843114 Solving 0.01937150237 + x = 0.625843114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01937150237' to each side of the equation. 0.01937150237 + -0.01937150237 + x = 0.625843114 + -0.01937150237 Combine like terms: 0.01937150237 + -0.01937150237 = 0.00000000000 0.00000000000 + x = 0.625843114 + -0.01937150237 x = 0.625843114 + -0.01937150237 Combine like terms: 0.625843114 + -0.01937150237 = 0.60647161163 x = 0.60647161163 Simplifying x = 0.60647161163

Subproblem 2

x + 0.01937150237 = -0.625843114 Simplifying x + 0.01937150237 = -0.625843114 Reorder the terms: 0.01937150237 + x = -0.625843114 Solving 0.01937150237 + x = -0.625843114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01937150237' to each side of the equation. 0.01937150237 + -0.01937150237 + x = -0.625843114 + -0.01937150237 Combine like terms: 0.01937150237 + -0.01937150237 = 0.00000000000 0.00000000000 + x = -0.625843114 + -0.01937150237 x = -0.625843114 + -0.01937150237 Combine like terms: -0.625843114 + -0.01937150237 = -0.64521461637 x = -0.64521461637 Simplifying x = -0.64521461637

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.60647161163, -0.64521461637}

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