9x^2+61x+14=0

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Solution for 9x^2+61x+14=0 equation:


Simplifying
9x2 + 61x + 14 = 0

Reorder the terms:
14 + 61x + 9x2 = 0

Solving
14 + 61x + 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'.
1.555555556 + 6.777777778x + x2 = 0

Move the constant term to the right:

Add '-1.555555556' to each side of the equation.
1.555555556 + 6.777777778x + -1.555555556 + x2 = 0 + -1.555555556

Reorder the terms:
1.555555556 + -1.555555556 + 6.777777778x + x2 = 0 + -1.555555556

Combine like terms: 1.555555556 + -1.555555556 = 0.000000000
0.000000000 + 6.777777778x + x2 = 0 + -1.555555556
6.777777778x + x2 = 0 + -1.555555556

Combine like terms: 0 + -1.555555556 = -1.555555556
6.777777778x + x2 = -1.555555556

The x term is 6.777777778x.  Take half its coefficient (3.388888889).
Square it (11.48456790) and add it to both sides.

Add '11.48456790' to each side of the equation.
6.777777778x + 11.48456790 + x2 = -1.555555556 + 11.48456790

Reorder the terms:
11.48456790 + 6.777777778x + x2 = -1.555555556 + 11.48456790

Combine like terms: -1.555555556 + 11.48456790 = 9.929012344
11.48456790 + 6.777777778x + x2 = 9.929012344

Factor a perfect square on the left side:
(x + 3.388888889)(x + 3.388888889) = 9.929012344

Calculate the square root of the right side: 3.151033536

Break this problem into two subproblems by setting 
(x + 3.388888889) equal to 3.151033536 and -3.151033536.

Subproblem 1

x + 3.388888889 = 3.151033536 Simplifying x + 3.388888889 = 3.151033536 Reorder the terms: 3.388888889 + x = 3.151033536 Solving 3.388888889 + x = 3.151033536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = 3.151033536 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = 3.151033536 + -3.388888889 x = 3.151033536 + -3.388888889 Combine like terms: 3.151033536 + -3.388888889 = -0.237855353 x = -0.237855353 Simplifying x = -0.237855353

Subproblem 2

x + 3.388888889 = -3.151033536 Simplifying x + 3.388888889 = -3.151033536 Reorder the terms: 3.388888889 + x = -3.151033536 Solving 3.388888889 + x = -3.151033536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = -3.151033536 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = -3.151033536 + -3.388888889 x = -3.151033536 + -3.388888889 Combine like terms: -3.151033536 + -3.388888889 = -6.539922425 x = -6.539922425 Simplifying x = -6.539922425

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.237855353, -6.539922425}

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