5x*x-30x+8=0

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Solution for 5x*x-30x+8=0 equation:


Simplifying
5x * x + -30x + 8 = 0

Multiply x * x
5x2 + -30x + 8 = 0

Reorder the terms:
8 + -30x + 5x2 = 0

Solving
8 + -30x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.6 + -6x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -6x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -6x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -6x + x2 = 0 + -1.6
-6x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-6x + x2 = -1.6

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1.6 + 9

Reorder the terms:
9 + -6x + x2 = -1.6 + 9

Combine like terms: -1.6 + 9 = 7.4
9 + -6x + x2 = 7.4

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.4

Calculate the square root of the right side: 2.720294102

Break this problem into two subproblems by setting 
(x + -3) equal to 2.720294102 and -2.720294102.

Subproblem 1

x + -3 = 2.720294102 Simplifying x + -3 = 2.720294102 Reorder the terms: -3 + x = 2.720294102 Solving -3 + x = 2.720294102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.720294102 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.720294102 + 3 x = 2.720294102 + 3 Combine like terms: 2.720294102 + 3 = 5.720294102 x = 5.720294102 Simplifying x = 5.720294102

Subproblem 2

x + -3 = -2.720294102 Simplifying x + -3 = -2.720294102 Reorder the terms: -3 + x = -2.720294102 Solving -3 + x = -2.720294102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.720294102 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.720294102 + 3 x = -2.720294102 + 3 Combine like terms: -2.720294102 + 3 = 0.279705898 x = 0.279705898 Simplifying x = 0.279705898

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.720294102, 0.279705898}

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