x^2-32x+68=0

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Solution for x^2-32x+68=0 equation:


Simplifying
x2 + -32x + 68 = 0

Reorder the terms:
68 + -32x + x2 = 0

Solving
68 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-68' to each side of the equation.
68 + -32x + -68 + x2 = 0 + -68

Reorder the terms:
68 + -68 + -32x + x2 = 0 + -68

Combine like terms: 68 + -68 = 0
0 + -32x + x2 = 0 + -68
-32x + x2 = 0 + -68

Combine like terms: 0 + -68 = -68
-32x + x2 = -68

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -68 + 256

Reorder the terms:
256 + -32x + x2 = -68 + 256

Combine like terms: -68 + 256 = 188
256 + -32x + x2 = 188

Factor a perfect square on the left side:
(x + -16)(x + -16) = 188

Calculate the square root of the right side: 13.711309201

Break this problem into two subproblems by setting 
(x + -16) equal to 13.711309201 and -13.711309201.

Subproblem 1

x + -16 = 13.711309201 Simplifying x + -16 = 13.711309201 Reorder the terms: -16 + x = 13.711309201 Solving -16 + x = 13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 13.711309201 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.711309201 + 16 x = 13.711309201 + 16 Combine like terms: 13.711309201 + 16 = 29.711309201 x = 29.711309201 Simplifying x = 29.711309201

Subproblem 2

x + -16 = -13.711309201 Simplifying x + -16 = -13.711309201 Reorder the terms: -16 + x = -13.711309201 Solving -16 + x = -13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -13.711309201 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.711309201 + 16 x = -13.711309201 + 16 Combine like terms: -13.711309201 + 16 = 2.288690799 x = 2.288690799 Simplifying x = 2.288690799

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.711309201, 2.288690799}

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