-3x^2+800x+20=

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Solution for -3x^2+800x+20= equation:


Simplifying
-3x2 + 800x + 20 = 0

Reorder the terms:
20 + 800x + -3x2 = 0

Solving
20 + 800x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-6.666666667 + -266.6666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -266.6666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -266.6666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -266.6666667x + x2 = 0 + 6.666666667
-266.6666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-266.6666667x + x2 = 6.666666667

The x term is -266.6666667x.  Take half its coefficient (-133.3333334).
Square it (17777.77780) and add it to both sides.

Add '17777.77780' to each side of the equation.
-266.6666667x + 17777.77780 + x2 = 6.666666667 + 17777.77780

Reorder the terms:
17777.77780 + -266.6666667x + x2 = 6.666666667 + 17777.77780

Combine like terms: 6.666666667 + 17777.77780 = 17784.444466667
17777.77780 + -266.6666667x + x2 = 17784.444466667

Factor a perfect square on the left side:
(x + -133.3333334)(x + -133.3333334) = 17784.444466667

Calculate the square root of the right side: 133.358331073

Break this problem into two subproblems by setting 
(x + -133.3333334) equal to 133.358331073 and -133.358331073.

Subproblem 1

x + -133.3333334 = 133.358331073 Simplifying x + -133.3333334 = 133.358331073 Reorder the terms: -133.3333334 + x = 133.358331073 Solving -133.3333334 + x = 133.358331073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = 133.358331073 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = 133.358331073 + 133.3333334 x = 133.358331073 + 133.3333334 Combine like terms: 133.358331073 + 133.3333334 = 266.691664473 x = 266.691664473 Simplifying x = 266.691664473

Subproblem 2

x + -133.3333334 = -133.358331073 Simplifying x + -133.3333334 = -133.358331073 Reorder the terms: -133.3333334 + x = -133.358331073 Solving -133.3333334 + x = -133.358331073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = -133.358331073 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = -133.358331073 + 133.3333334 x = -133.358331073 + 133.3333334 Combine like terms: -133.358331073 + 133.3333334 = -0.024997673 x = -0.024997673 Simplifying x = -0.024997673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {266.691664473, -0.024997673}

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