25=0021x^2-.286x+16.28

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Solution for 25=0021x^2-.286x+16.28 equation:


Simplifying
25 = 21x2 + -0.286x + 16.28

Reorder the terms:
25 = 16.28 + -0.286x + 21x2

Solving
25 = 16.28 + -0.286x + 21x2

Solving for variable 'x'.

Combine like terms: 25 + -16.28 = 8.72
8.72 + 0.286x + -21x2 = 16.28 + -0.286x + 21x2 + -16.28 + 0.286x + -21x2

Reorder the terms:
8.72 + 0.286x + -21x2 = 16.28 + -16.28 + -0.286x + 0.286x + 21x2 + -21x2

Combine like terms: 16.28 + -16.28 = 0.00
8.72 + 0.286x + -21x2 = 0.00 + -0.286x + 0.286x + 21x2 + -21x2
8.72 + 0.286x + -21x2 = -0.286x + 0.286x + 21x2 + -21x2

Combine like terms: -0.286x + 0.286x = 0.000
8.72 + 0.286x + -21x2 = 0.000 + 21x2 + -21x2
8.72 + 0.286x + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
8.72 + 0.286x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-0.4152380952 + -0.01361904762x + x2 = 0

Move the constant term to the right:

Add '0.4152380952' to each side of the equation.
-0.4152380952 + -0.01361904762x + 0.4152380952 + x2 = 0 + 0.4152380952

Reorder the terms:
-0.4152380952 + 0.4152380952 + -0.01361904762x + x2 = 0 + 0.4152380952

Combine like terms: -0.4152380952 + 0.4152380952 = 0.0000000000
0.0000000000 + -0.01361904762x + x2 = 0 + 0.4152380952
-0.01361904762x + x2 = 0 + 0.4152380952

Combine like terms: 0 + 0.4152380952 = 0.4152380952
-0.01361904762x + x2 = 0.4152380952

The x term is -0.01361904762x.  Take half its coefficient (-0.00680952381).
Square it (0.00004636961452) and add it to both sides.

Add '0.00004636961452' to each side of the equation.
-0.01361904762x + 0.00004636961452 + x2 = 0.4152380952 + 0.00004636961452

Reorder the terms:
0.00004636961452 + -0.01361904762x + x2 = 0.4152380952 + 0.00004636961452

Combine like terms: 0.4152380952 + 0.00004636961452 = 0.41528446481452
0.00004636961452 + -0.01361904762x + x2 = 0.41528446481452

Factor a perfect square on the left side:
(x + -0.00680952381)(x + -0.00680952381) = 0.41528446481452

Calculate the square root of the right side: 0.644425686

Break this problem into two subproblems by setting 
(x + -0.00680952381) equal to 0.644425686 and -0.644425686.

Subproblem 1

x + -0.00680952381 = 0.644425686 Simplifying x + -0.00680952381 = 0.644425686 Reorder the terms: -0.00680952381 + x = 0.644425686 Solving -0.00680952381 + x = 0.644425686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00680952381' to each side of the equation. -0.00680952381 + 0.00680952381 + x = 0.644425686 + 0.00680952381 Combine like terms: -0.00680952381 + 0.00680952381 = 0.00000000000 0.00000000000 + x = 0.644425686 + 0.00680952381 x = 0.644425686 + 0.00680952381 Combine like terms: 0.644425686 + 0.00680952381 = 0.65123520981 x = 0.65123520981 Simplifying x = 0.65123520981

Subproblem 2

x + -0.00680952381 = -0.644425686 Simplifying x + -0.00680952381 = -0.644425686 Reorder the terms: -0.00680952381 + x = -0.644425686 Solving -0.00680952381 + x = -0.644425686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00680952381' to each side of the equation. -0.00680952381 + 0.00680952381 + x = -0.644425686 + 0.00680952381 Combine like terms: -0.00680952381 + 0.00680952381 = 0.00000000000 0.00000000000 + x = -0.644425686 + 0.00680952381 x = -0.644425686 + 0.00680952381 Combine like terms: -0.644425686 + 0.00680952381 = -0.63761616219 x = -0.63761616219 Simplifying x = -0.63761616219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.65123520981, -0.63761616219}

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