x^2-16x=-51

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Solution for x^2-16x=-51 equation:


Simplifying
x2 + -16x = -51

Reorder the terms:
-16x + x2 = -51

Solving
-16x + x2 = -51

Solving for variable 'x'.

Reorder the terms:
51 + -16x + x2 = -51 + 51

Combine like terms: -51 + 51 = 0
51 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + -16x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + -16x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -16x + x2 = 0 + -51
-16x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
-16x + x2 = -51

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 = -51 + 64

Reorder the terms:
64 + -16x + x2 = -51 + 64

Combine like terms: -51 + 64 = 13
64 + -16x + x2 = 13

Factor a perfect square on the left side:
(x + -8)(x + -8) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -8) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -8 = 3.605551275 Simplifying x + -8 = 3.605551275 Reorder the terms: -8 + x = 3.605551275 Solving -8 + x = 3.605551275 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 = 3.605551275 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.605551275 + 8 x = 3.605551275 + 8 Combine like terms: 3.605551275 + 8 = 11.605551275 x = 11.605551275 Simplifying x = 11.605551275

Subproblem 2

x + -8 = -3.605551275 Simplifying x + -8 = -3.605551275 Reorder the terms: -8 + x = -3.605551275 Solving -8 + x = -3.605551275 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 = -3.605551275 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.605551275 + 8 x = -3.605551275 + 8 Combine like terms: -3.605551275 + 8 = 4.394448725 x = 4.394448725 Simplifying x = 4.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.605551275, 4.394448725}

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