3x^2+5x=432

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Solution for 3x^2+5x=432 equation:


Simplifying
3x2 + 5x = 432

Reorder the terms:
5x + 3x2 = 432

Solving
5x + 3x2 = 432

Solving for variable 'x'.

Reorder the terms:
-432 + 5x + 3x2 = 432 + -432

Combine like terms: 432 + -432 = 0
-432 + 5x + 3x2 = 0

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

Divide each side by '3'.
-144 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 1.666666667x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 1.666666667x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 1.666666667x + x2 = 0 + 144
1.666666667x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
1.666666667x + x2 = 144

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 = 144 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 144 + 0.6944444447

Combine like terms: 144 + 0.6944444447 = 144.6944444447
0.6944444447 + 1.666666667x + x2 = 144.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 144.6944444447

Calculate the square root of the right side: 12.028900384

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 12.028900384 and -12.028900384.

Subproblem 1

x + 0.8333333335 = 12.028900384 Simplifying x + 0.8333333335 = 12.028900384 Reorder the terms: 0.8333333335 + x = 12.028900384 Solving 0.8333333335 + x = 12.028900384 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 = 12.028900384 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 12.028900384 + -0.8333333335 x = 12.028900384 + -0.8333333335 Combine like terms: 12.028900384 + -0.8333333335 = 11.1955670505 x = 11.1955670505 Simplifying x = 11.1955670505

Subproblem 2

x + 0.8333333335 = -12.028900384 Simplifying x + 0.8333333335 = -12.028900384 Reorder the terms: 0.8333333335 + x = -12.028900384 Solving 0.8333333335 + x = -12.028900384 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 = -12.028900384 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -12.028900384 + -0.8333333335 x = -12.028900384 + -0.8333333335 Combine like terms: -12.028900384 + -0.8333333335 = -12.8622337175 x = -12.8622337175 Simplifying x = -12.8622337175

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.1955670505, -12.8622337175}

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