3x^2+5x=18

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Solution for 3x^2+5x=18 equation:


Simplifying
3x2 + 5x = 18

Reorder the terms:
5x + 3x2 = 18

Solving
5x + 3x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 5x + 3x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 5x + 3x2 = 0

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

Divide each side by '3'.
-6 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 1.666666667x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 1.666666667x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 1.666666667x + x2 = 0 + 6
1.666666667x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
1.666666667x + x2 = 6

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 = 6 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 6 + 0.6944444447

Combine like terms: 6 + 0.6944444447 = 6.6944444447
0.6944444447 + 1.666666667x + x2 = 6.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 6.6944444447

Calculate the square root of the right side: 2.587362449

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.587362449 and -2.587362449.

Subproblem 1

x + 0.8333333335 = 2.587362449 Simplifying x + 0.8333333335 = 2.587362449 Reorder the terms: 0.8333333335 + x = 2.587362449 Solving 0.8333333335 + x = 2.587362449 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 = 2.587362449 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.587362449 + -0.8333333335 x = 2.587362449 + -0.8333333335 Combine like terms: 2.587362449 + -0.8333333335 = 1.7540291155 x = 1.7540291155 Simplifying x = 1.7540291155

Subproblem 2

x + 0.8333333335 = -2.587362449 Simplifying x + 0.8333333335 = -2.587362449 Reorder the terms: 0.8333333335 + x = -2.587362449 Solving 0.8333333335 + x = -2.587362449 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 = -2.587362449 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.587362449 + -0.8333333335 x = -2.587362449 + -0.8333333335 Combine like terms: -2.587362449 + -0.8333333335 = -3.4206957825 x = -3.4206957825 Simplifying x = -3.4206957825

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7540291155, -3.4206957825}

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