x^2+34x+192=285

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Solution for x^2+34x+192=285 equation:


Simplifying
x2 + 34x + 192 = 285

Reorder the terms:
192 + 34x + x2 = 285

Solving
192 + 34x + x2 = 285

Solving for variable 'x'.

Reorder the terms:
192 + -285 + 34x + x2 = 285 + -285

Combine like terms: 192 + -285 = -93
-93 + 34x + x2 = 285 + -285

Combine like terms: 285 + -285 = 0
-93 + 34x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 34x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + 34x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 34x + x2 = 0 + 93
34x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
34x + x2 = 93

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 = 93 + 289

Reorder the terms:
289 + 34x + x2 = 93 + 289

Combine like terms: 93 + 289 = 382
289 + 34x + x2 = 382

Factor a perfect square on the left side:
(x + 17)(x + 17) = 382

Calculate the square root of the right side: 19.544820286

Break this problem into two subproblems by setting 
(x + 17) equal to 19.544820286 and -19.544820286.

Subproblem 1

x + 17 = 19.544820286 Simplifying x + 17 = 19.544820286 Reorder the terms: 17 + x = 19.544820286 Solving 17 + x = 19.544820286 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 = 19.544820286 + -17 Combine like terms: 17 + -17 = 0 0 + x = 19.544820286 + -17 x = 19.544820286 + -17 Combine like terms: 19.544820286 + -17 = 2.544820286 x = 2.544820286 Simplifying x = 2.544820286

Subproblem 2

x + 17 = -19.544820286 Simplifying x + 17 = -19.544820286 Reorder the terms: 17 + x = -19.544820286 Solving 17 + x = -19.544820286 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 = -19.544820286 + -17 Combine like terms: 17 + -17 = 0 0 + x = -19.544820286 + -17 x = -19.544820286 + -17 Combine like terms: -19.544820286 + -17 = -36.544820286 x = -36.544820286 Simplifying x = -36.544820286

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.544820286, -36.544820286}

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