2x^2-39=10x

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Solution for 2x^2-39=10x equation:


Simplifying
2x2 + -39 = 10x

Reorder the terms:
-39 + 2x2 = 10x

Solving
-39 + 2x2 = 10x

Solving for variable 'x'.

Reorder the terms:
-39 + -10x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-39 + -10x + 2x2 = 0

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

Divide each side by '2'.
-19.5 + -5x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + -5x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + -5x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + -5x + x2 = 0 + 19.5
-5x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
-5x + x2 = 19.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 19.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 19.5 + 6.25

Combine like terms: 19.5 + 6.25 = 25.75
6.25 + -5x + x2 = 25.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 25.75

Calculate the square root of the right side: 5.074445783

Break this problem into two subproblems by setting 
(x + -2.5) equal to 5.074445783 and -5.074445783.

Subproblem 1

x + -2.5 = 5.074445783 Simplifying x + -2.5 = 5.074445783 Reorder the terms: -2.5 + x = 5.074445783 Solving -2.5 + x = 5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.074445783 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.074445783 + 2.5 x = 5.074445783 + 2.5 Combine like terms: 5.074445783 + 2.5 = 7.574445783 x = 7.574445783 Simplifying x = 7.574445783

Subproblem 2

x + -2.5 = -5.074445783 Simplifying x + -2.5 = -5.074445783 Reorder the terms: -2.5 + x = -5.074445783 Solving -2.5 + x = -5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.074445783 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.074445783 + 2.5 x = -5.074445783 + 2.5 Combine like terms: -5.074445783 + 2.5 = -2.574445783 x = -2.574445783 Simplifying x = -2.574445783

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.574445783, -2.574445783}

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