81+(2x-3)=x^2

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Solution for 81+(2x-3)=x^2 equation:


Simplifying
81 + (2x + -3) = x2

Reorder the terms:
81 + (-3 + 2x) = x2

Remove parenthesis around (-3 + 2x)
81 + -3 + 2x = x2

Combine like terms: 81 + -3 = 78
78 + 2x = x2

Solving
78 + 2x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
78 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-78 + -2x + x2 = 0

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + -2x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + -2x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + -2x + x2 = 0 + 78
-2x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
-2x + x2 = 78

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 78 + 1

Reorder the terms:
1 + -2x + x2 = 78 + 1

Combine like terms: 78 + 1 = 79
1 + -2x + x2 = 79

Factor a perfect square on the left side:
(x + -1)(x + -1) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + -1) equal to 8.888194417 and -8.888194417.

Subproblem 1

x + -1 = 8.888194417 Simplifying x + -1 = 8.888194417 Reorder the terms: -1 + x = 8.888194417 Solving -1 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.888194417 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.888194417 + 1 x = 8.888194417 + 1 Combine like terms: 8.888194417 + 1 = 9.888194417 x = 9.888194417 Simplifying x = 9.888194417

Subproblem 2

x + -1 = -8.888194417 Simplifying x + -1 = -8.888194417 Reorder the terms: -1 + x = -8.888194417 Solving -1 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.888194417 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.888194417 + 1 x = -8.888194417 + 1 Combine like terms: -8.888194417 + 1 = -7.888194417 x = -7.888194417 Simplifying x = -7.888194417

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.888194417, -7.888194417}

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