3x^2+5x-360=0

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Solution for 3x^2+5x-360=0 equation:


Simplifying
3x2 + 5x + -360 = 0

Reorder the terms:
-360 + 5x + 3x2 = 0

Solving
-360 + 5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-120 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 1.666666667x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 1.666666667x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 1.666666667x + x2 = 0 + 120
1.666666667x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
1.666666667x + x2 = 120

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 120 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 120 + 0.6944444447

Combine like terms: 120 + 0.6944444447 = 120.6944444447
0.6944444447 + 1.666666667x + x2 = 120.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 120.6944444447

Calculate the square root of the right side: 10.986102332

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 10.986102332 and -10.986102332.

Subproblem 1

x + 0.8333333335 = 10.986102332 Simplifying x + 0.8333333335 = 10.986102332 Reorder the terms: 0.8333333335 + x = 10.986102332 Solving 0.8333333335 + x = 10.986102332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 10.986102332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 10.986102332 + -0.8333333335 x = 10.986102332 + -0.8333333335 Combine like terms: 10.986102332 + -0.8333333335 = 10.1527689985 x = 10.1527689985 Simplifying x = 10.1527689985

Subproblem 2

x + 0.8333333335 = -10.986102332 Simplifying x + 0.8333333335 = -10.986102332 Reorder the terms: 0.8333333335 + x = -10.986102332 Solving 0.8333333335 + x = -10.986102332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -10.986102332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -10.986102332 + -0.8333333335 x = -10.986102332 + -0.8333333335 Combine like terms: -10.986102332 + -0.8333333335 = -11.8194356655 x = -11.8194356655 Simplifying x = -11.8194356655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.1527689985, -11.8194356655}

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