18+5x^2=20x

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Solution for 18+5x^2=20x equation:


Simplifying
18 + 5x2 = 20x

Solving
18 + 5x2 = 20x

Solving for variable 'x'.

Reorder the terms:
18 + -20x + 5x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
18 + -20x + 5x2 = 0

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

Divide each side by '5'.
3.6 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + -4x + -3.6 + x2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + -4x + x2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + -4x + x2 = 0 + -3.6
-4x + x2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
-4x + x2 = -3.6

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.6 + 4

Reorder the terms:
4 + -4x + x2 = -3.6 + 4

Combine like terms: -3.6 + 4 = 0.4
4 + -4x + x2 = 0.4

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + -2) equal to 0.632455532 and -0.632455532.

Subproblem 1

x + -2 = 0.632455532 Simplifying x + -2 = 0.632455532 Reorder the terms: -2 + x = 0.632455532 Solving -2 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.632455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.632455532 + 2 x = 0.632455532 + 2 Combine like terms: 0.632455532 + 2 = 2.632455532 x = 2.632455532 Simplifying x = 2.632455532

Subproblem 2

x + -2 = -0.632455532 Simplifying x + -2 = -0.632455532 Reorder the terms: -2 + x = -0.632455532 Solving -2 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.632455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.632455532 + 2 x = -0.632455532 + 2 Combine like terms: -0.632455532 + 2 = 1.367544468 x = 1.367544468 Simplifying x = 1.367544468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.632455532, 1.367544468}

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