x^2+142-24x=0

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Solution for x^2+142-24x=0 equation:


Simplifying
x2 + 142 + -24x = 0

Reorder the terms:
142 + -24x + x2 = 0

Solving
142 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-142' to each side of the equation.
142 + -24x + -142 + x2 = 0 + -142

Reorder the terms:
142 + -142 + -24x + x2 = 0 + -142

Combine like terms: 142 + -142 = 0
0 + -24x + x2 = 0 + -142
-24x + x2 = 0 + -142

Combine like terms: 0 + -142 = -142
-24x + x2 = -142

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -142 + 144

Reorder the terms:
144 + -24x + x2 = -142 + 144

Combine like terms: -142 + 144 = 2
144 + -24x + x2 = 2

Factor a perfect square on the left side:
(x + -12)(x + -12) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -12) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + -12 = 1.414213562 Simplifying x + -12 = 1.414213562 Reorder the terms: -12 + x = 1.414213562 Solving -12 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 1.414213562 + 12 Combine like terms: -12 + 12 = 0 0 + x = 1.414213562 + 12 x = 1.414213562 + 12 Combine like terms: 1.414213562 + 12 = 13.414213562 x = 13.414213562 Simplifying x = 13.414213562

Subproblem 2

x + -12 = -1.414213562 Simplifying x + -12 = -1.414213562 Reorder the terms: -12 + x = -1.414213562 Solving -12 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -1.414213562 + 12 Combine like terms: -12 + 12 = 0 0 + x = -1.414213562 + 12 x = -1.414213562 + 12 Combine like terms: -1.414213562 + 12 = 10.585786438 x = 10.585786438 Simplifying x = 10.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.414213562, 10.585786438}

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