3x^2-28x-18=0

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Solution for 3x^2-28x-18=0 equation:


Simplifying
3x2 + -28x + -18 = 0

Reorder the terms:
-18 + -28x + 3x2 = 0

Solving
-18 + -28x + 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'.
-6 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -9.333333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -9.333333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -9.333333333x + x2 = 0 + 6
-9.333333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-9.333333333x + x2 = 6

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 6 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 6 + 21.77777778

Combine like terms: 6 + 21.77777778 = 27.77777778
21.77777778 + -9.333333333x + x2 = 27.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 27.77777778

Calculate the square root of the right side: 5.270462767

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 5.270462767 and -5.270462767.

Subproblem 1

x + -4.666666667 = 5.270462767 Simplifying x + -4.666666667 = 5.270462767 Reorder the terms: -4.666666667 + x = 5.270462767 Solving -4.666666667 + x = 5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 5.270462767 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 5.270462767 + 4.666666667 x = 5.270462767 + 4.666666667 Combine like terms: 5.270462767 + 4.666666667 = 9.937129434 x = 9.937129434 Simplifying x = 9.937129434

Subproblem 2

x + -4.666666667 = -5.270462767 Simplifying x + -4.666666667 = -5.270462767 Reorder the terms: -4.666666667 + x = -5.270462767 Solving -4.666666667 + x = -5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -5.270462767 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -5.270462767 + 4.666666667 x = -5.270462767 + 4.666666667 Combine like terms: -5.270462767 + 4.666666667 = -0.6037961 x = -0.6037961 Simplifying x = -0.6037961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.937129434, -0.6037961}

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