x^2-68x+578=0

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Solution for x^2-68x+578=0 equation:


Simplifying
x2 + -68x + 578 = 0

Reorder the terms:
578 + -68x + x2 = 0

Solving
578 + -68x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-578' to each side of the equation.
578 + -68x + -578 + x2 = 0 + -578

Reorder the terms:
578 + -578 + -68x + x2 = 0 + -578

Combine like terms: 578 + -578 = 0
0 + -68x + x2 = 0 + -578
-68x + x2 = 0 + -578

Combine like terms: 0 + -578 = -578
-68x + x2 = -578

The x term is -68x.  Take half its coefficient (-34).
Square it (1156) and add it to both sides.

Add '1156' to each side of the equation.
-68x + 1156 + x2 = -578 + 1156

Reorder the terms:
1156 + -68x + x2 = -578 + 1156

Combine like terms: -578 + 1156 = 578
1156 + -68x + x2 = 578

Factor a perfect square on the left side:
(x + -34)(x + -34) = 578

Calculate the square root of the right side: 24.04163056

Break this problem into two subproblems by setting 
(x + -34) equal to 24.04163056 and -24.04163056.

Subproblem 1

x + -34 = 24.04163056 Simplifying x + -34 = 24.04163056 Reorder the terms: -34 + x = 24.04163056 Solving -34 + x = 24.04163056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = 24.04163056 + 34 Combine like terms: -34 + 34 = 0 0 + x = 24.04163056 + 34 x = 24.04163056 + 34 Combine like terms: 24.04163056 + 34 = 58.04163056 x = 58.04163056 Simplifying x = 58.04163056

Subproblem 2

x + -34 = -24.04163056 Simplifying x + -34 = -24.04163056 Reorder the terms: -34 + x = -24.04163056 Solving -34 + x = -24.04163056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = -24.04163056 + 34 Combine like terms: -34 + 34 = 0 0 + x = -24.04163056 + 34 x = -24.04163056 + 34 Combine like terms: -24.04163056 + 34 = 9.95836944 x = 9.95836944 Simplifying x = 9.95836944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {58.04163056, 9.95836944}

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