2x^2=13x+21

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Solution for 2x^2=13x+21 equation:


Simplifying
2x2 = 13x + 21

Reorder the terms:
2x2 = 21 + 13x

Solving
2x2 = 21 + 13x

Solving for variable 'x'.

Reorder the terms:
-21 + -13x + 2x2 = 21 + 13x + -21 + -13x

Reorder the terms:
-21 + -13x + 2x2 = 21 + -21 + 13x + -13x

Combine like terms: 21 + -21 = 0
-21 + -13x + 2x2 = 0 + 13x + -13x
-21 + -13x + 2x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-21 + -13x + 2x2 = 0

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

Divide each side by '2'.
-10.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -6.5x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -6.5x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -6.5x + x2 = 0 + 10.5
-6.5x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-6.5x + x2 = 10.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 10.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 10.5 + 10.5625

Combine like terms: 10.5 + 10.5625 = 21.0625
10.5625 + -6.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.589389938 and -4.589389938.

Subproblem 1

x + -3.25 = 4.589389938 Simplifying x + -3.25 = 4.589389938 Reorder the terms: -3.25 + x = 4.589389938 Solving -3.25 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.589389938 + 3.25 x = 4.589389938 + 3.25 Combine like terms: 4.589389938 + 3.25 = 7.839389938 x = 7.839389938 Simplifying x = 7.839389938

Subproblem 2

x + -3.25 = -4.589389938 Simplifying x + -3.25 = -4.589389938 Reorder the terms: -3.25 + x = -4.589389938 Solving -3.25 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.589389938 + 3.25 x = -4.589389938 + 3.25 Combine like terms: -4.589389938 + 3.25 = -1.339389938 x = -1.339389938 Simplifying x = -1.339389938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.839389938, -1.339389938}

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