5x^2-30x+12=0

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Solution for 5x^2-30x+12=0 equation:


Simplifying
5x2 + -30x + 12 = 0

Reorder the terms:
12 + -30x + 5x2 = 0

Solving
12 + -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'.
2.4 + -6x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -6x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -6x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -6x + x2 = 0 + -2.4
-6x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-6x + x2 = -2.4

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 = -2.4 + 9

Reorder the terms:
9 + -6x + x2 = -2.4 + 9

Combine like terms: -2.4 + 9 = 6.6
9 + -6x + x2 = 6.6

Factor a perfect square on the left side:
(x + -3)(x + -3) = 6.6

Calculate the square root of the right side: 2.569046516

Break this problem into two subproblems by setting 
(x + -3) equal to 2.569046516 and -2.569046516.

Subproblem 1

x + -3 = 2.569046516 Simplifying x + -3 = 2.569046516 Reorder the terms: -3 + x = 2.569046516 Solving -3 + x = 2.569046516 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 = 2.569046516 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.569046516 + 3 x = 2.569046516 + 3 Combine like terms: 2.569046516 + 3 = 5.569046516 x = 5.569046516 Simplifying x = 5.569046516

Subproblem 2

x + -3 = -2.569046516 Simplifying x + -3 = -2.569046516 Reorder the terms: -3 + x = -2.569046516 Solving -3 + x = -2.569046516 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 = -2.569046516 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.569046516 + 3 x = -2.569046516 + 3 Combine like terms: -2.569046516 + 3 = 0.430953484 x = 0.430953484 Simplifying x = 0.430953484

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.569046516, 0.430953484}

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