x(9x+58)=49

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Solution for x(9x+58)=49 equation:


Simplifying
x(9x + 58) = 49

Reorder the terms:
x(58 + 9x) = 49
(58 * x + 9x * x) = 49
(58x + 9x2) = 49

Solving
58x + 9x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + 58x + 9x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 58x + 9x2 = 0

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

Divide each side by '9'.
-5.444444444 + 6.444444444x + x2 = 0

Move the constant term to the right:

Add '5.444444444' to each side of the equation.
-5.444444444 + 6.444444444x + 5.444444444 + x2 = 0 + 5.444444444

Reorder the terms:
-5.444444444 + 5.444444444 + 6.444444444x + x2 = 0 + 5.444444444

Combine like terms: -5.444444444 + 5.444444444 = 0.000000000
0.000000000 + 6.444444444x + x2 = 0 + 5.444444444
6.444444444x + x2 = 0 + 5.444444444

Combine like terms: 0 + 5.444444444 = 5.444444444
6.444444444x + x2 = 5.444444444

The x term is 6.444444444x.  Take half its coefficient (3.222222222).
Square it (10.38271605) and add it to both sides.

Add '10.38271605' to each side of the equation.
6.444444444x + 10.38271605 + x2 = 5.444444444 + 10.38271605

Reorder the terms:
10.38271605 + 6.444444444x + x2 = 5.444444444 + 10.38271605

Combine like terms: 5.444444444 + 10.38271605 = 15.827160494
10.38271605 + 6.444444444x + x2 = 15.827160494

Factor a perfect square on the left side:
(x + 3.222222222)(x + 3.222222222) = 15.827160494

Calculate the square root of the right side: 3.978336398

Break this problem into two subproblems by setting 
(x + 3.222222222) equal to 3.978336398 and -3.978336398.

Subproblem 1

x + 3.222222222 = 3.978336398 Simplifying x + 3.222222222 = 3.978336398 Reorder the terms: 3.222222222 + x = 3.978336398 Solving 3.222222222 + x = 3.978336398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.222222222' to each side of the equation. 3.222222222 + -3.222222222 + x = 3.978336398 + -3.222222222 Combine like terms: 3.222222222 + -3.222222222 = 0.000000000 0.000000000 + x = 3.978336398 + -3.222222222 x = 3.978336398 + -3.222222222 Combine like terms: 3.978336398 + -3.222222222 = 0.756114176 x = 0.756114176 Simplifying x = 0.756114176

Subproblem 2

x + 3.222222222 = -3.978336398 Simplifying x + 3.222222222 = -3.978336398 Reorder the terms: 3.222222222 + x = -3.978336398 Solving 3.222222222 + x = -3.978336398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.222222222' to each side of the equation. 3.222222222 + -3.222222222 + x = -3.978336398 + -3.222222222 Combine like terms: 3.222222222 + -3.222222222 = 0.000000000 0.000000000 + x = -3.978336398 + -3.222222222 x = -3.978336398 + -3.222222222 Combine like terms: -3.978336398 + -3.222222222 = -7.20055862 x = -7.20055862 Simplifying x = -7.20055862

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.756114176, -7.20055862}

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