x^2+3x=120

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


Simplifying
x2 + 3x = 120

Reorder the terms:
3x + x2 = 120

Solving
3x + x2 = 120

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 3x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 3x + x2 = 0 + 120

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

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

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 120 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 120 + 2.25

Combine like terms: 120 + 2.25 = 122.25
2.25 + 3x + x2 = 122.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11.056672194 and -11.056672194.

Subproblem 1

x + 1.5 = 11.056672194 Simplifying x + 1.5 = 11.056672194 Reorder the terms: 1.5 + x = 11.056672194 Solving 1.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.056672194 + -1.5 x = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 x = 9.556672194 Simplifying x = 9.556672194

Subproblem 2

x + 1.5 = -11.056672194 Simplifying x + 1.5 = -11.056672194 Reorder the terms: 1.5 + x = -11.056672194 Solving 1.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.056672194 + -1.5 x = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 x = -12.556672194 Simplifying x = -12.556672194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.556672194, -12.556672194}

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