5x^2-22x=8

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


Simplifying
5x2 + -22x = 8

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

Solving
-22x + 5x2 = 8

Solving for variable 'x'.

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is -4.4x.  Take half its coefficient (-2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
-4.4x + 4.84 + x2 = 1.6 + 4.84

Reorder the terms:
4.84 + -4.4x + x2 = 1.6 + 4.84

Combine like terms: 1.6 + 4.84 = 6.44
4.84 + -4.4x + x2 = 6.44

Factor a perfect square on the left side:
(x + -2.2)(x + -2.2) = 6.44

Calculate the square root of the right side: 2.537715508

Break this problem into two subproblems by setting 
(x + -2.2) equal to 2.537715508 and -2.537715508.

Subproblem 1

x + -2.2 = 2.537715508 Simplifying x + -2.2 = 2.537715508 Reorder the terms: -2.2 + x = 2.537715508 Solving -2.2 + x = 2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 2.537715508 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.537715508 + 2.2 x = 2.537715508 + 2.2 Combine like terms: 2.537715508 + 2.2 = 4.737715508 x = 4.737715508 Simplifying x = 4.737715508

Subproblem 2

x + -2.2 = -2.537715508 Simplifying x + -2.2 = -2.537715508 Reorder the terms: -2.2 + x = -2.537715508 Solving -2.2 + x = -2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -2.537715508 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.537715508 + 2.2 x = -2.537715508 + 2.2 Combine like terms: -2.537715508 + 2.2 = -0.337715508 x = -0.337715508 Simplifying x = -0.337715508

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.737715508, -0.337715508}

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