9x^2+30x=68

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Solution for 9x^2+30x=68 equation:


Simplifying
9x2 + 30x = 68

Reorder the terms:
30x + 9x2 = 68

Solving
30x + 9x2 = 68

Solving for variable 'x'.

Reorder the terms:
-68 + 30x + 9x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-68 + 30x + 9x2 = 0

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

Divide each side by '9'.
-7.555555556 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '7.555555556' to each side of the equation.
-7.555555556 + 3.333333333x + 7.555555556 + x2 = 0 + 7.555555556

Reorder the terms:
-7.555555556 + 7.555555556 + 3.333333333x + x2 = 0 + 7.555555556

Combine like terms: -7.555555556 + 7.555555556 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 7.555555556
3.333333333x + x2 = 0 + 7.555555556

Combine like terms: 0 + 7.555555556 = 7.555555556
3.333333333x + x2 = 7.555555556

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 7.555555556 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 7.555555556 + 2.777777779

Combine like terms: 7.555555556 + 2.777777779 = 10.333333335
2.777777779 + 3.333333333x + x2 = 10.333333335

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 10.333333335

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.214550254 and -3.214550254.

Subproblem 1

x + 1.666666667 = 3.214550254 Simplifying x + 1.666666667 = 3.214550254 Reorder the terms: 1.666666667 + x = 3.214550254 Solving 1.666666667 + x = 3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 3.214550254 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.214550254 + -1.666666667 x = 3.214550254 + -1.666666667 Combine like terms: 3.214550254 + -1.666666667 = 1.547883587 x = 1.547883587 Simplifying x = 1.547883587

Subproblem 2

x + 1.666666667 = -3.214550254 Simplifying x + 1.666666667 = -3.214550254 Reorder the terms: 1.666666667 + x = -3.214550254 Solving 1.666666667 + x = -3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -3.214550254 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.214550254 + -1.666666667 x = -3.214550254 + -1.666666667 Combine like terms: -3.214550254 + -1.666666667 = -4.881216921 x = -4.881216921 Simplifying x = -4.881216921

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.547883587, -4.881216921}

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