3x^2+17x+15=0

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Solution for 3x^2+17x+15=0 equation:


Simplifying
3x2 + 17x + 15 = 0

Reorder the terms:
15 + 17x + 3x2 = 0

Solving
15 + 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'.
5 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5.666666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 5.666666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5.666666667x + x2 = 0 + -5
5.666666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
5.666666667x + x2 = -5

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 = -5 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -5 + 8.027777782

Combine like terms: -5 + 8.027777782 = 3.027777782
8.027777782 + 5.666666667x + x2 = 3.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 3.027777782

Calculate the square root of the right side: 1.740051086

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 1.740051086 and -1.740051086.

Subproblem 1

x + 2.833333334 = 1.740051086 Simplifying x + 2.833333334 = 1.740051086 Reorder the terms: 2.833333334 + x = 1.740051086 Solving 2.833333334 + x = 1.740051086 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 = 1.740051086 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 1.740051086 + -2.833333334 x = 1.740051086 + -2.833333334 Combine like terms: 1.740051086 + -2.833333334 = -1.093282248 x = -1.093282248 Simplifying x = -1.093282248

Subproblem 2

x + 2.833333334 = -1.740051086 Simplifying x + 2.833333334 = -1.740051086 Reorder the terms: 2.833333334 + x = -1.740051086 Solving 2.833333334 + x = -1.740051086 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 = -1.740051086 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -1.740051086 + -2.833333334 x = -1.740051086 + -2.833333334 Combine like terms: -1.740051086 + -2.833333334 = -4.57338442 x = -4.57338442 Simplifying x = -4.57338442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.093282248, -4.57338442}

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