3x^2+10x=120

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Solution for 3x^2+10x=120 equation:


Simplifying
3x2 + 10x = 120

Reorder the terms:
10x + 3x2 = 120

Solving
10x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 10x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 10x + 3x2 = 0

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

Divide each side by '3'.
-40 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 3.333333333x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 3.333333333x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 3.333333333x + x2 = 0 + 40
3.333333333x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
3.333333333x + x2 = 40

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 = 40 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 40 + 2.777777779

Combine like terms: 40 + 2.777777779 = 42.777777779
2.777777779 + 3.333333333x + x2 = 42.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 42.777777779

Calculate the square root of the right side: 6.54047229

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 6.54047229 and -6.54047229.

Subproblem 1

x + 1.666666667 = 6.54047229 Simplifying x + 1.666666667 = 6.54047229 Reorder the terms: 1.666666667 + x = 6.54047229 Solving 1.666666667 + x = 6.54047229 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 = 6.54047229 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 6.54047229 + -1.666666667 x = 6.54047229 + -1.666666667 Combine like terms: 6.54047229 + -1.666666667 = 4.873805623 x = 4.873805623 Simplifying x = 4.873805623

Subproblem 2

x + 1.666666667 = -6.54047229 Simplifying x + 1.666666667 = -6.54047229 Reorder the terms: 1.666666667 + x = -6.54047229 Solving 1.666666667 + x = -6.54047229 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 = -6.54047229 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -6.54047229 + -1.666666667 x = -6.54047229 + -1.666666667 Combine like terms: -6.54047229 + -1.666666667 = -8.207138957 x = -8.207138957 Simplifying x = -8.207138957

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.873805623, -8.207138957}

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