9x^2+29x+10=0

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Solution for 9x^2+29x+10=0 equation:


Simplifying
9x2 + 29x + 10 = 0

Reorder the terms:
10 + 29x + 9x2 = 0

Solving
10 + 29x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
1.111111111 + 3.222222222x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + 3.222222222x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + 3.222222222x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + 3.222222222x + x2 = 0 + -1.111111111
3.222222222x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
3.222222222x + x2 = -1.111111111

The x term is 3.222222222x.  Take half its coefficient (1.611111111).
Square it (2.595679012) and add it to both sides.

Add '2.595679012' to each side of the equation.
3.222222222x + 2.595679012 + x2 = -1.111111111 + 2.595679012

Reorder the terms:
2.595679012 + 3.222222222x + x2 = -1.111111111 + 2.595679012

Combine like terms: -1.111111111 + 2.595679012 = 1.484567901
2.595679012 + 3.222222222x + x2 = 1.484567901

Factor a perfect square on the left side:
(x + 1.611111111)(x + 1.611111111) = 1.484567901

Calculate the square root of the right side: 1.218428455

Break this problem into two subproblems by setting 
(x + 1.611111111) equal to 1.218428455 and -1.218428455.

Subproblem 1

x + 1.611111111 = 1.218428455 Simplifying x + 1.611111111 = 1.218428455 Reorder the terms: 1.611111111 + x = 1.218428455 Solving 1.611111111 + x = 1.218428455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = 1.218428455 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = 1.218428455 + -1.611111111 x = 1.218428455 + -1.611111111 Combine like terms: 1.218428455 + -1.611111111 = -0.392682656 x = -0.392682656 Simplifying x = -0.392682656

Subproblem 2

x + 1.611111111 = -1.218428455 Simplifying x + 1.611111111 = -1.218428455 Reorder the terms: 1.611111111 + x = -1.218428455 Solving 1.611111111 + x = -1.218428455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = -1.218428455 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = -1.218428455 + -1.611111111 x = -1.218428455 + -1.611111111 Combine like terms: -1.218428455 + -1.611111111 = -2.829539566 x = -2.829539566 Simplifying x = -2.829539566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.392682656, -2.829539566}

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