5x^2-22=8x

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Solution for 5x^2-22=8x equation:


Simplifying
5x2 + -22 = 8x

Reorder the terms:
-22 + 5x2 = 8x

Solving
-22 + 5x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-22 + -8x + 5x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-22 + -8x + 5x2 = 0

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

Divide each side by '5'.
-4.4 + -1.6x + x2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + -1.6x + 4.4 + x2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + -1.6x + x2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + -1.6x + x2 = 0 + 4.4
-1.6x + x2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
-1.6x + x2 = 4.4

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 4.4 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 4.4 + 0.64

Combine like terms: 4.4 + 0.64 = 5.04
0.64 + -1.6x + x2 = 5.04

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 5.04

Calculate the square root of the right side: 2.244994432

Break this problem into two subproblems by setting 
(x + -0.8) equal to 2.244994432 and -2.244994432.

Subproblem 1

x + -0.8 = 2.244994432 Simplifying x + -0.8 = 2.244994432 Reorder the terms: -0.8 + x = 2.244994432 Solving -0.8 + x = 2.244994432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.244994432 + 0.8 x = 2.244994432 + 0.8 Combine like terms: 2.244994432 + 0.8 = 3.044994432 x = 3.044994432 Simplifying x = 3.044994432

Subproblem 2

x + -0.8 = -2.244994432 Simplifying x + -0.8 = -2.244994432 Reorder the terms: -0.8 + x = -2.244994432 Solving -0.8 + x = -2.244994432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.244994432 + 0.8 x = -2.244994432 + 0.8 Combine like terms: -2.244994432 + 0.8 = -1.444994432 x = -1.444994432 Simplifying x = -1.444994432

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.044994432, -1.444994432}

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