4x^2-1800=x+1800

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Solution for 4x^2-1800=x+1800 equation:


Simplifying
4x2 + -1800 = x + 1800

Reorder the terms:
-1800 + 4x2 = x + 1800

Reorder the terms:
-1800 + 4x2 = 1800 + x

Solving
-1800 + 4x2 = 1800 + x

Solving for variable 'x'.

Reorder the terms:
-1800 + -1800 + -1x + 4x2 = 1800 + x + -1800 + -1x

Combine like terms: -1800 + -1800 = -3600
-3600 + -1x + 4x2 = 1800 + x + -1800 + -1x

Reorder the terms:
-3600 + -1x + 4x2 = 1800 + -1800 + x + -1x

Combine like terms: 1800 + -1800 = 0
-3600 + -1x + 4x2 = 0 + x + -1x
-3600 + -1x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-3600 + -1x + 4x2 = 0

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

Divide each side by '4'.
-900 + -0.25x + x2 = 0

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + -0.25x + 900 + x2 = 0 + 900

Reorder the terms:
-900 + 900 + -0.25x + x2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + -0.25x + x2 = 0 + 900
-0.25x + x2 = 0 + 900

Combine like terms: 0 + 900 = 900
-0.25x + x2 = 900

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 900 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 900 + 0.015625

Combine like terms: 900 + 0.015625 = 900.015625
0.015625 + -0.25x + x2 = 900.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 900.015625

Calculate the square root of the right side: 30.000260416

Break this problem into two subproblems by setting 
(x + -0.125) equal to 30.000260416 and -30.000260416.

Subproblem 1

x + -0.125 = 30.000260416 Simplifying x + -0.125 = 30.000260416 Reorder the terms: -0.125 + x = 30.000260416 Solving -0.125 + x = 30.000260416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 30.000260416 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 30.000260416 + 0.125 x = 30.000260416 + 0.125 Combine like terms: 30.000260416 + 0.125 = 30.125260416 x = 30.125260416 Simplifying x = 30.125260416

Subproblem 2

x + -0.125 = -30.000260416 Simplifying x + -0.125 = -30.000260416 Reorder the terms: -0.125 + x = -30.000260416 Solving -0.125 + x = -30.000260416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -30.000260416 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -30.000260416 + 0.125 x = -30.000260416 + 0.125 Combine like terms: -30.000260416 + 0.125 = -29.875260416 x = -29.875260416 Simplifying x = -29.875260416

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.125260416, -29.875260416}

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