34x+84-x^2=0

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Solution for 34x+84-x^2=0 equation:


Simplifying
34x + 84 + -1x2 = 0

Reorder the terms:
84 + 34x + -1x2 = 0

Solving
84 + 34x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-84 + -34x + x2 = 0

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -34x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -34x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -34x + x2 = 0 + 84
-34x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-34x + x2 = 84

The x term is -34x.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x + 289 + x2 = 84 + 289

Reorder the terms:
289 + -34x + x2 = 84 + 289

Combine like terms: 84 + 289 = 373
289 + -34x + x2 = 373

Factor a perfect square on the left side:
(x + -17)(x + -17) = 373

Calculate the square root of the right side: 19.313207916

Break this problem into two subproblems by setting 
(x + -17) equal to 19.313207916 and -19.313207916.

Subproblem 1

x + -17 = 19.313207916 Simplifying x + -17 = 19.313207916 Reorder the terms: -17 + x = 19.313207916 Solving -17 + x = 19.313207916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 19.313207916 + 17 Combine like terms: -17 + 17 = 0 0 + x = 19.313207916 + 17 x = 19.313207916 + 17 Combine like terms: 19.313207916 + 17 = 36.313207916 x = 36.313207916 Simplifying x = 36.313207916

Subproblem 2

x + -17 = -19.313207916 Simplifying x + -17 = -19.313207916 Reorder the terms: -17 + x = -19.313207916 Solving -17 + x = -19.313207916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -19.313207916 + 17 Combine like terms: -17 + 17 = 0 0 + x = -19.313207916 + 17 x = -19.313207916 + 17 Combine like terms: -19.313207916 + 17 = -2.313207916 x = -2.313207916 Simplifying x = -2.313207916

Solution

The solution to the problem is based on the solutions from the subproblems. x = {36.313207916, -2.313207916}

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