2x^2-43x=21

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Solution for 2x^2-43x=21 equation:


Simplifying
2x2 + -43x = 21

Reorder the terms:
-43x + 2x2 = 21

Solving
-43x + 2x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -43x + 2x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -43x + 2x2 = 0

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

Divide each side by '2'.
-10.5 + -21.5x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -21.5x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -21.5x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -21.5x + x2 = 0 + 10.5
-21.5x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-21.5x + x2 = 10.5

The x term is -21.5x.  Take half its coefficient (-10.75).
Square it (115.5625) and add it to both sides.

Add '115.5625' to each side of the equation.
-21.5x + 115.5625 + x2 = 10.5 + 115.5625

Reorder the terms:
115.5625 + -21.5x + x2 = 10.5 + 115.5625

Combine like terms: 10.5 + 115.5625 = 126.0625
115.5625 + -21.5x + x2 = 126.0625

Factor a perfect square on the left side:
(x + -10.75)(x + -10.75) = 126.0625

Calculate the square root of the right side: 11.227755786

Break this problem into two subproblems by setting 
(x + -10.75) equal to 11.227755786 and -11.227755786.

Subproblem 1

x + -10.75 = 11.227755786 Simplifying x + -10.75 = 11.227755786 Reorder the terms: -10.75 + x = 11.227755786 Solving -10.75 + x = 11.227755786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = 11.227755786 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = 11.227755786 + 10.75 x = 11.227755786 + 10.75 Combine like terms: 11.227755786 + 10.75 = 21.977755786 x = 21.977755786 Simplifying x = 21.977755786

Subproblem 2

x + -10.75 = -11.227755786 Simplifying x + -10.75 = -11.227755786 Reorder the terms: -10.75 + x = -11.227755786 Solving -10.75 + x = -11.227755786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = -11.227755786 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = -11.227755786 + 10.75 x = -11.227755786 + 10.75 Combine like terms: -11.227755786 + 10.75 = -0.477755786 x = -0.477755786 Simplifying x = -0.477755786

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.977755786, -0.477755786}

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