2x^2-50x=x^2+2x+36

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Solution for 2x^2-50x=x^2+2x+36 equation:


Simplifying
2x2 + -50x = x2 + 2x + 36

Reorder the terms:
-50x + 2x2 = x2 + 2x + 36

Reorder the terms:
-50x + 2x2 = 36 + 2x + x2

Solving
-50x + 2x2 = 36 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-36 + -50x + -2x + 2x2 + -1x2 = 36 + 2x + x2 + -36 + -2x + -1x2

Combine like terms: -50x + -2x = -52x
-36 + -52x + 2x2 + -1x2 = 36 + 2x + x2 + -36 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-36 + -52x + 1x2 = 36 + 2x + x2 + -36 + -2x + -1x2

Reorder the terms:
-36 + -52x + 1x2 = 36 + -36 + 2x + -2x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-36 + -52x + 1x2 = 0 + 2x + -2x + x2 + -1x2
-36 + -52x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-36 + -52x + 1x2 = 0 + x2 + -1x2
-36 + -52x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -52x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -52x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -52x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -52x + x2 = 0 + 36
-52x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-52x + x2 = 36

The x term is -52x.  Take half its coefficient (-26).
Square it (676) and add it to both sides.

Add '676' to each side of the equation.
-52x + 676 + x2 = 36 + 676

Reorder the terms:
676 + -52x + x2 = 36 + 676

Combine like terms: 36 + 676 = 712
676 + -52x + x2 = 712

Factor a perfect square on the left side:
(x + -26)(x + -26) = 712

Calculate the square root of the right side: 26.683328128

Break this problem into two subproblems by setting 
(x + -26) equal to 26.683328128 and -26.683328128.

Subproblem 1

x + -26 = 26.683328128 Simplifying x + -26 = 26.683328128 Reorder the terms: -26 + x = 26.683328128 Solving -26 + x = 26.683328128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 26.683328128 + 26 Combine like terms: -26 + 26 = 0 0 + x = 26.683328128 + 26 x = 26.683328128 + 26 Combine like terms: 26.683328128 + 26 = 52.683328128 x = 52.683328128 Simplifying x = 52.683328128

Subproblem 2

x + -26 = -26.683328128 Simplifying x + -26 = -26.683328128 Reorder the terms: -26 + x = -26.683328128 Solving -26 + x = -26.683328128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -26.683328128 + 26 Combine like terms: -26 + 26 = 0 0 + x = -26.683328128 + 26 x = -26.683328128 + 26 Combine like terms: -26.683328128 + 26 = -0.683328128 x = -0.683328128 Simplifying x = -0.683328128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {52.683328128, -0.683328128}

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