x^2-6x+16=7+2x

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Solution for x^2-6x+16=7+2x equation:


Simplifying
x2 + -6x + 16 = 7 + 2x

Reorder the terms:
16 + -6x + x2 = 7 + 2x

Solving
16 + -6x + x2 = 7 + 2x

Solving for variable 'x'.

Reorder the terms:
16 + -7 + -6x + -2x + x2 = 7 + 2x + -7 + -2x

Combine like terms: 16 + -7 = 9
9 + -6x + -2x + x2 = 7 + 2x + -7 + -2x

Combine like terms: -6x + -2x = -8x
9 + -8x + x2 = 7 + 2x + -7 + -2x

Reorder the terms:
9 + -8x + x2 = 7 + -7 + 2x + -2x

Combine like terms: 7 + -7 = 0
9 + -8x + x2 = 0 + 2x + -2x
9 + -8x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
9 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -8x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8x + x2 = 0 + -9
-8x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8x + x2 = -9

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -9 + 16

Reorder the terms:
16 + -8x + x2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8x + x2 = 7

Factor a perfect square on the left side:
(x + -4)(x + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -4 = 2.645751311 Simplifying x + -4 = 2.645751311 Reorder the terms: -4 + x = 2.645751311 Solving -4 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.645751311 + 4 x = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 x = 6.645751311 Simplifying x = 6.645751311

Subproblem 2

x + -4 = -2.645751311 Simplifying x + -4 = -2.645751311 Reorder the terms: -4 + x = -2.645751311 Solving -4 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.645751311 + 4 x = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 x = 1.354248689 Simplifying x = 1.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.645751311, 1.354248689}

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