30x^2-89x+30=0

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Solution for 30x^2-89x+30=0 equation:


Simplifying
30x2 + -89x + 30 = 0

Reorder the terms:
30 + -89x + 30x2 = 0

Solving
30 + -89x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
1 + -2.966666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.966666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.966666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.966666667x + x2 = 0 + -1
-2.966666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.966666667x + x2 = -1

The x term is -2.966666667x.  Take half its coefficient (-1.483333334).
Square it (2.200277780) and add it to both sides.

Add '2.200277780' to each side of the equation.
-2.966666667x + 2.200277780 + x2 = -1 + 2.200277780

Reorder the terms:
2.200277780 + -2.966666667x + x2 = -1 + 2.200277780

Combine like terms: -1 + 2.200277780 = 1.20027778
2.200277780 + -2.966666667x + x2 = 1.20027778

Factor a perfect square on the left side:
(x + -1.483333334)(x + -1.483333334) = 1.20027778

Calculate the square root of the right side: 1.095571896

Break this problem into two subproblems by setting 
(x + -1.483333334) equal to 1.095571896 and -1.095571896.

Subproblem 1

x + -1.483333334 = 1.095571896 Simplifying x + -1.483333334 = 1.095571896 Reorder the terms: -1.483333334 + x = 1.095571896 Solving -1.483333334 + x = 1.095571896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.483333334' to each side of the equation. -1.483333334 + 1.483333334 + x = 1.095571896 + 1.483333334 Combine like terms: -1.483333334 + 1.483333334 = 0.000000000 0.000000000 + x = 1.095571896 + 1.483333334 x = 1.095571896 + 1.483333334 Combine like terms: 1.095571896 + 1.483333334 = 2.57890523 x = 2.57890523 Simplifying x = 2.57890523

Subproblem 2

x + -1.483333334 = -1.095571896 Simplifying x + -1.483333334 = -1.095571896 Reorder the terms: -1.483333334 + x = -1.095571896 Solving -1.483333334 + x = -1.095571896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.483333334' to each side of the equation. -1.483333334 + 1.483333334 + x = -1.095571896 + 1.483333334 Combine like terms: -1.483333334 + 1.483333334 = 0.000000000 0.000000000 + x = -1.095571896 + 1.483333334 x = -1.095571896 + 1.483333334 Combine like terms: -1.095571896 + 1.483333334 = 0.387761438 x = 0.387761438 Simplifying x = 0.387761438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.57890523, 0.387761438}

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