3x^2+17x-3=0

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Solution for 3x^2+17x-3=0 equation:


Simplifying
3x2 + 17x + -3 = 0

Reorder the terms:
-3 + 17x + 3x2 = 0

Solving
-3 + 17x + 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'.
-1 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 5.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5.666666667x + x2 = 0 + 1
5.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
5.666666667x + x2 = 1

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = 1 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = 1 + 8.027777782

Combine like terms: 1 + 8.027777782 = 9.027777782
8.027777782 + 5.666666667x + x2 = 9.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 9.027777782

Calculate the square root of the right side: 3.004626064

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 3.004626064 and -3.004626064.

Subproblem 1

x + 2.833333334 = 3.004626064 Simplifying x + 2.833333334 = 3.004626064 Reorder the terms: 2.833333334 + x = 3.004626064 Solving 2.833333334 + x = 3.004626064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 3.004626064 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.004626064 + -2.833333334 x = 3.004626064 + -2.833333334 Combine like terms: 3.004626064 + -2.833333334 = 0.17129273 x = 0.17129273 Simplifying x = 0.17129273

Subproblem 2

x + 2.833333334 = -3.004626064 Simplifying x + 2.833333334 = -3.004626064 Reorder the terms: 2.833333334 + x = -3.004626064 Solving 2.833333334 + x = -3.004626064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -3.004626064 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.004626064 + -2.833333334 x = -3.004626064 + -2.833333334 Combine like terms: -3.004626064 + -2.833333334 = -5.837959398 x = -5.837959398 Simplifying x = -5.837959398

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.17129273, -5.837959398}

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