2x^2+62.8x=1000

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Solution for 2x^2+62.8x=1000 equation:


Simplifying
2x2 + 62.8x = 1000

Reorder the terms:
62.8x + 2x2 = 1000

Solving
62.8x + 2x2 = 1000

Solving for variable 'x'.

Reorder the terms:
-1000 + 62.8x + 2x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 62.8x + 2x2 = 0

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

Divide each side by '2'.
-500 + 31.4x + x2 = 0

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 31.4x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 31.4x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 31.4x + x2 = 0 + 500
31.4x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
31.4x + x2 = 500

The x term is 31.4x.  Take half its coefficient (15.7).
Square it (246.49) and add it to both sides.

Add '246.49' to each side of the equation.
31.4x + 246.49 + x2 = 500 + 246.49

Reorder the terms:
246.49 + 31.4x + x2 = 500 + 246.49

Combine like terms: 500 + 246.49 = 746.49
246.49 + 31.4x + x2 = 746.49

Factor a perfect square on the left side:
(x + 15.7)(x + 15.7) = 746.49

Calculate the square root of the right side: 27.321969182

Break this problem into two subproblems by setting 
(x + 15.7) equal to 27.321969182 and -27.321969182.

Subproblem 1

x + 15.7 = 27.321969182 Simplifying x + 15.7 = 27.321969182 Reorder the terms: 15.7 + x = 27.321969182 Solving 15.7 + x = 27.321969182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.7' to each side of the equation. 15.7 + -15.7 + x = 27.321969182 + -15.7 Combine like terms: 15.7 + -15.7 = 0.0 0.0 + x = 27.321969182 + -15.7 x = 27.321969182 + -15.7 Combine like terms: 27.321969182 + -15.7 = 11.621969182 x = 11.621969182 Simplifying x = 11.621969182

Subproblem 2

x + 15.7 = -27.321969182 Simplifying x + 15.7 = -27.321969182 Reorder the terms: 15.7 + x = -27.321969182 Solving 15.7 + x = -27.321969182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.7' to each side of the equation. 15.7 + -15.7 + x = -27.321969182 + -15.7 Combine like terms: 15.7 + -15.7 = 0.0 0.0 + x = -27.321969182 + -15.7 x = -27.321969182 + -15.7 Combine like terms: -27.321969182 + -15.7 = -43.021969182 x = -43.021969182 Simplifying x = -43.021969182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.621969182, -43.021969182}

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