9x^2-332x-1600=0

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Solution for 9x^2-332x-1600=0 equation:


Simplifying
9x2 + -332x + -1600 = 0

Reorder the terms:
-1600 + -332x + 9x2 = 0

Solving
-1600 + -332x + 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'.
-177.7777778 + -36.88888889x + x2 = 0

Move the constant term to the right:

Add '177.7777778' to each side of the equation.
-177.7777778 + -36.88888889x + 177.7777778 + x2 = 0 + 177.7777778

Reorder the terms:
-177.7777778 + 177.7777778 + -36.88888889x + x2 = 0 + 177.7777778

Combine like terms: -177.7777778 + 177.7777778 = 0.0000000
0.0000000 + -36.88888889x + x2 = 0 + 177.7777778
-36.88888889x + x2 = 0 + 177.7777778

Combine like terms: 0 + 177.7777778 = 177.7777778
-36.88888889x + x2 = 177.7777778

The x term is -36.88888889x.  Take half its coefficient (-18.44444445).
Square it (340.1975311) and add it to both sides.

Add '340.1975311' to each side of the equation.
-36.88888889x + 340.1975311 + x2 = 177.7777778 + 340.1975311

Reorder the terms:
340.1975311 + -36.88888889x + x2 = 177.7777778 + 340.1975311

Combine like terms: 177.7777778 + 340.1975311 = 517.9753089
340.1975311 + -36.88888889x + x2 = 517.9753089

Factor a perfect square on the left side:
(x + -18.44444445)(x + -18.44444445) = 517.9753089

Calculate the square root of the right side: 22.759070915

Break this problem into two subproblems by setting 
(x + -18.44444445) equal to 22.759070915 and -22.759070915.

Subproblem 1

x + -18.44444445 = 22.759070915 Simplifying x + -18.44444445 = 22.759070915 Reorder the terms: -18.44444445 + x = 22.759070915 Solving -18.44444445 + x = 22.759070915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.44444445' to each side of the equation. -18.44444445 + 18.44444445 + x = 22.759070915 + 18.44444445 Combine like terms: -18.44444445 + 18.44444445 = 0.00000000 0.00000000 + x = 22.759070915 + 18.44444445 x = 22.759070915 + 18.44444445 Combine like terms: 22.759070915 + 18.44444445 = 41.203515365 x = 41.203515365 Simplifying x = 41.203515365

Subproblem 2

x + -18.44444445 = -22.759070915 Simplifying x + -18.44444445 = -22.759070915 Reorder the terms: -18.44444445 + x = -22.759070915 Solving -18.44444445 + x = -22.759070915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.44444445' to each side of the equation. -18.44444445 + 18.44444445 + x = -22.759070915 + 18.44444445 Combine like terms: -18.44444445 + 18.44444445 = 0.00000000 0.00000000 + x = -22.759070915 + 18.44444445 x = -22.759070915 + 18.44444445 Combine like terms: -22.759070915 + 18.44444445 = -4.314626465 x = -4.314626465 Simplifying x = -4.314626465

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.203515365, -4.314626465}

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