477.21=-16x^2+200x+4

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Solution for 477.21=-16x^2+200x+4 equation:


Simplifying
477.21 = -16x2 + 200x + 4

Reorder the terms:
477.21 = 4 + 200x + -16x2

Solving
477.21 = 4 + 200x + -16x2

Solving for variable 'x'.

Combine like terms: 477.21 + -4 = 473.21
473.21 + -200x + 16x2 = 4 + 200x + -16x2 + -4 + -200x + 16x2

Reorder the terms:
473.21 + -200x + 16x2 = 4 + -4 + 200x + -200x + -16x2 + 16x2

Combine like terms: 4 + -4 = 0
473.21 + -200x + 16x2 = 0 + 200x + -200x + -16x2 + 16x2
473.21 + -200x + 16x2 = 200x + -200x + -16x2 + 16x2

Combine like terms: 200x + -200x = 0
473.21 + -200x + 16x2 = 0 + -16x2 + 16x2
473.21 + -200x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
473.21 + -200x + 16x2 = 0

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

Divide each side by '16'.
29.575625 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-29.575625' to each side of the equation.
29.575625 + -12.5x + -29.575625 + x2 = 0 + -29.575625

Reorder the terms:
29.575625 + -29.575625 + -12.5x + x2 = 0 + -29.575625

Combine like terms: 29.575625 + -29.575625 = 0.000000
0.000000 + -12.5x + x2 = 0 + -29.575625
-12.5x + x2 = 0 + -29.575625

Combine like terms: 0 + -29.575625 = -29.575625
-12.5x + x2 = -29.575625

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -29.575625 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -29.575625 + 39.0625

Combine like terms: -29.575625 + 39.0625 = 9.486875
39.0625 + -12.5x + x2 = 9.486875

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 9.486875

Calculate the square root of the right side: 3.080077109

Break this problem into two subproblems by setting 
(x + -6.25) equal to 3.080077109 and -3.080077109.

Subproblem 1

x + -6.25 = 3.080077109 Simplifying x + -6.25 = 3.080077109 Reorder the terms: -6.25 + x = 3.080077109 Solving -6.25 + x = 3.080077109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 3.080077109 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 3.080077109 + 6.25 x = 3.080077109 + 6.25 Combine like terms: 3.080077109 + 6.25 = 9.330077109 x = 9.330077109 Simplifying x = 9.330077109

Subproblem 2

x + -6.25 = -3.080077109 Simplifying x + -6.25 = -3.080077109 Reorder the terms: -6.25 + x = -3.080077109 Solving -6.25 + x = -3.080077109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -3.080077109 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -3.080077109 + 6.25 x = -3.080077109 + 6.25 Combine like terms: -3.080077109 + 6.25 = 3.169922891 x = 3.169922891 Simplifying x = 3.169922891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.330077109, 3.169922891}

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