3x^2+30x=22

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Solution for 3x^2+30x=22 equation:


Simplifying
3x2 + 30x = 22

Reorder the terms:
30x + 3x2 = 22

Solving
30x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 30x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 30x + 3x2 = 0

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

Divide each side by '3'.
-7.333333333 + 10x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 10x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 10x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 10x + x2 = 0 + 7.333333333
10x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
10x + x2 = 7.333333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 7.333333333 + 25

Reorder the terms:
25 + 10x + x2 = 7.333333333 + 25

Combine like terms: 7.333333333 + 25 = 32.333333333
25 + 10x + x2 = 32.333333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 32.333333333

Calculate the square root of the right side: 5.686240703

Break this problem into two subproblems by setting 
(x + 5) equal to 5.686240703 and -5.686240703.

Subproblem 1

x + 5 = 5.686240703 Simplifying x + 5 = 5.686240703 Reorder the terms: 5 + x = 5.686240703 Solving 5 + x = 5.686240703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.686240703 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.686240703 + -5 x = 5.686240703 + -5 Combine like terms: 5.686240703 + -5 = 0.686240703 x = 0.686240703 Simplifying x = 0.686240703

Subproblem 2

x + 5 = -5.686240703 Simplifying x + 5 = -5.686240703 Reorder the terms: 5 + x = -5.686240703 Solving 5 + x = -5.686240703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.686240703 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.686240703 + -5 x = -5.686240703 + -5 Combine like terms: -5.686240703 + -5 = -10.686240703 x = -10.686240703 Simplifying x = -10.686240703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.686240703, -10.686240703}

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