x^2-24x+58=0

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Solution for x^2-24x+58=0 equation:


Simplifying
x2 + -24x + 58 = 0

Reorder the terms:
58 + -24x + x2 = 0

Solving
58 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-58' to each side of the equation.
58 + -24x + -58 + x2 = 0 + -58

Reorder the terms:
58 + -58 + -24x + x2 = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -24x + x2 = 0 + -58
-24x + x2 = 0 + -58

Combine like terms: 0 + -58 = -58
-24x + x2 = -58

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 = -58 + 144

Reorder the terms:
144 + -24x + x2 = -58 + 144

Combine like terms: -58 + 144 = 86
144 + -24x + x2 = 86

Factor a perfect square on the left side:
(x + -12)(x + -12) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -12) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -12 = 9.273618495 Simplifying x + -12 = 9.273618495 Reorder the terms: -12 + x = 9.273618495 Solving -12 + x = 9.273618495 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 = 9.273618495 + 12 Combine like terms: -12 + 12 = 0 0 + x = 9.273618495 + 12 x = 9.273618495 + 12 Combine like terms: 9.273618495 + 12 = 21.273618495 x = 21.273618495 Simplifying x = 21.273618495

Subproblem 2

x + -12 = -9.273618495 Simplifying x + -12 = -9.273618495 Reorder the terms: -12 + x = -9.273618495 Solving -12 + x = -9.273618495 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 = -9.273618495 + 12 Combine like terms: -12 + 12 = 0 0 + x = -9.273618495 + 12 x = -9.273618495 + 12 Combine like terms: -9.273618495 + 12 = 2.726381505 x = 2.726381505 Simplifying x = 2.726381505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.273618495, 2.726381505}

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