3x^2-10+7x=180

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Solution for 3x^2-10+7x=180 equation: 


Simplifying
3x2 + -10 + 7x = 180

Reorder the terms:
-10 + 7x + 3x2 = 180

Solving
-10 + 7x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-10 + -180 + 7x + 3x2 = 180 + -180

Combine like terms: -10 + -180 = -190
-190 + 7x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-190 + 7x + 3x2 = 0

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

Divide each side by '3'.
-63.33333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '63.33333333' to each side of the equation.
-63.33333333 + 2.333333333x + 63.33333333 + x2 = 0 + 63.33333333

Reorder the terms:
-63.33333333 + 63.33333333 + 2.333333333x + x2 = 0 + 63.33333333

Combine like terms: -63.33333333 + 63.33333333 = 0.00000000
0.00000000 + 2.333333333x + x2 = 0 + 63.33333333
2.333333333x + x2 = 0 + 63.33333333

Combine like terms: 0 + 63.33333333 = 63.33333333
2.333333333x + x2 = 63.33333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 63.33333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 63.33333333 + 1.361111112

Combine like terms: 63.33333333 + 1.361111112 = 64.694444442
1.361111112 + 2.333333333x + x2 = 64.694444442

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 64.694444442

Calculate the square root of the right side: 8.043285675

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 8.043285675 and -8.043285675.


Subproblem 1
x + 1.166666667 = 8.043285675

Simplifying
x + 1.166666667 = 8.043285675

Reorder the terms:
1.166666667 + x = 8.043285675

Solving
1.166666667 + x = 8.043285675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 8.043285675 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 8.043285675 + -1.166666667
x = 8.043285675 + -1.166666667

Combine like terms: 8.043285675 + -1.166666667 = 6.876619008
x = 6.876619008

Simplifying
x = 6.876619008


Subproblem 2
x + 1.166666667 = -8.043285675

Simplifying
x + 1.166666667 = -8.043285675

Reorder the terms:
1.166666667 + x = -8.043285675

Solving
1.166666667 + x = -8.043285675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -8.043285675 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -8.043285675 + -1.166666667
x = -8.043285675 + -1.166666667

Combine like terms: -8.043285675 + -1.166666667 = -9.209952342
x = -9.209952342

Simplifying
x = -9.209952342


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.876619008, -9.209952342}

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