80=2.5x+.55x^2

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Solution for 80=2.5x+.55x^2 equation:


Simplifying
80 = 2.5x + 0.55x2

Solving
80 = 2.5x + 0.55x2

Solving for variable 'x'.

Reorder the terms:
80 + -2.5x + -0.55x2 = 2.5x + -2.5x + 0.55x2 + -0.55x2

Combine like terms: 2.5x + -2.5x = 0.0
80 + -2.5x + -0.55x2 = 0.0 + 0.55x2 + -0.55x2
80 + -2.5x + -0.55x2 = 0.55x2 + -0.55x2

Combine like terms: 0.55x2 + -0.55x2 = 0.00
80 + -2.5x + -0.55x2 = 0.00

Begin completing the square.  Divide all terms by
-0.55 the coefficient of the squared term: 

Divide each side by '-0.55'.
-145.4545455 + 4.545454545x + x2 = 0

Move the constant term to the right:

Add '145.4545455' to each side of the equation.
-145.4545455 + 4.545454545x + 145.4545455 + x2 = 0 + 145.4545455

Reorder the terms:
-145.4545455 + 145.4545455 + 4.545454545x + x2 = 0 + 145.4545455

Combine like terms: -145.4545455 + 145.4545455 = 0.0000000
0.0000000 + 4.545454545x + x2 = 0 + 145.4545455
4.545454545x + x2 = 0 + 145.4545455

Combine like terms: 0 + 145.4545455 = 145.4545455
4.545454545x + x2 = 145.4545455

The x term is 4.545454545x.  Take half its coefficient (2.272727273).
Square it (5.165289257) and add it to both sides.

Add '5.165289257' to each side of the equation.
4.545454545x + 5.165289257 + x2 = 145.4545455 + 5.165289257

Reorder the terms:
5.165289257 + 4.545454545x + x2 = 145.4545455 + 5.165289257

Combine like terms: 145.4545455 + 5.165289257 = 150.619834757
5.165289257 + 4.545454545x + x2 = 150.619834757

Factor a perfect square on the left side:
(x + 2.272727273)(x + 2.272727273) = 150.619834757

Calculate the square root of the right side: 12.272727275

Break this problem into two subproblems by setting 
(x + 2.272727273) equal to 12.272727275 and -12.272727275.

Subproblem 1

x + 2.272727273 = 12.272727275 Simplifying x + 2.272727273 = 12.272727275 Reorder the terms: 2.272727273 + x = 12.272727275 Solving 2.272727273 + x = 12.272727275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.272727273' to each side of the equation. 2.272727273 + -2.272727273 + x = 12.272727275 + -2.272727273 Combine like terms: 2.272727273 + -2.272727273 = 0.000000000 0.000000000 + x = 12.272727275 + -2.272727273 x = 12.272727275 + -2.272727273 Combine like terms: 12.272727275 + -2.272727273 = 10.000000002 x = 10.000000002 Simplifying x = 10.000000002

Subproblem 2

x + 2.272727273 = -12.272727275 Simplifying x + 2.272727273 = -12.272727275 Reorder the terms: 2.272727273 + x = -12.272727275 Solving 2.272727273 + x = -12.272727275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.272727273' to each side of the equation. 2.272727273 + -2.272727273 + x = -12.272727275 + -2.272727273 Combine like terms: 2.272727273 + -2.272727273 = 0.000000000 0.000000000 + x = -12.272727275 + -2.272727273 x = -12.272727275 + -2.272727273 Combine like terms: -12.272727275 + -2.272727273 = -14.545454548 x = -14.545454548 Simplifying x = -14.545454548

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.000000002, -14.545454548}

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