(x^2)-16x+58=0

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Solution for (x^2)-16x+58=0 equation:


Simplifying
(x2) + -16x + 58 = 0
x2 + -16x + 58 = 0

Reorder the terms:
58 + -16x + x2 = 0

Solving
58 + -16x + 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 + -16x + -58 + x2 = 0 + -58

Reorder the terms:
58 + -58 + -16x + x2 = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -16x + x2 = 0 + -58
-16x + x2 = 0 + -58

Combine like terms: 0 + -58 = -58
-16x + x2 = -58

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -58 + 64

Reorder the terms:
64 + -16x + x2 = -58 + 64

Combine like terms: -58 + 64 = 6
64 + -16x + x2 = 6

Factor a perfect square on the left side:
(x + -8)(x + -8) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -8) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + -8 = 2.449489743 Simplifying x + -8 = 2.449489743 Reorder the terms: -8 + x = 2.449489743 Solving -8 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 2.449489743 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.449489743 + 8 x = 2.449489743 + 8 Combine like terms: 2.449489743 + 8 = 10.449489743 x = 10.449489743 Simplifying x = 10.449489743

Subproblem 2

x + -8 = -2.449489743 Simplifying x + -8 = -2.449489743 Reorder the terms: -8 + x = -2.449489743 Solving -8 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -2.449489743 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.449489743 + 8 x = -2.449489743 + 8 Combine like terms: -2.449489743 + 8 = 5.550510257 x = 5.550510257 Simplifying x = 5.550510257

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.449489743, 5.550510257}

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