17a-2+3a^2=

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Solution for 17a-2+3a^2= equation:


Simplifying
17a + -2 + 3a2 = 0

Reorder the terms:
-2 + 17a + 3a2 = 0

Solving
-2 + 17a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-0.6666666667 + 5.666666667a + a2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 5.666666667a + 0.6666666667 + a2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 5.666666667a + a2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 5.666666667a + a2 = 0 + 0.6666666667
5.666666667a + a2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
5.666666667a + a2 = 0.6666666667

The a term is 5.666666667a.  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.
5.666666667a + 8.027777782 + a2 = 0.6666666667 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667a + a2 = 0.6666666667 + 8.027777782

Combine like terms: 0.6666666667 + 8.027777782 = 8.6944444487
8.027777782 + 5.666666667a + a2 = 8.6944444487

Factor a perfect square on the left side:
(a + 2.833333334)(a + 2.833333334) = 8.6944444487

Calculate the square root of the right side: 2.948634336

Break this problem into two subproblems by setting 
(a + 2.833333334) equal to 2.948634336 and -2.948634336.

Subproblem 1

a + 2.833333334 = 2.948634336 Simplifying a + 2.833333334 = 2.948634336 Reorder the terms: 2.833333334 + a = 2.948634336 Solving 2.833333334 + a = 2.948634336 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + a = 2.948634336 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + a = 2.948634336 + -2.833333334 a = 2.948634336 + -2.833333334 Combine like terms: 2.948634336 + -2.833333334 = 0.115301002 a = 0.115301002 Simplifying a = 0.115301002

Subproblem 2

a + 2.833333334 = -2.948634336 Simplifying a + 2.833333334 = -2.948634336 Reorder the terms: 2.833333334 + a = -2.948634336 Solving 2.833333334 + a = -2.948634336 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + a = -2.948634336 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + a = -2.948634336 + -2.833333334 a = -2.948634336 + -2.833333334 Combine like terms: -2.948634336 + -2.833333334 = -5.78196767 a = -5.78196767 Simplifying a = -5.78196767

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.115301002, -5.78196767}

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