9x-7=x^2

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Solution for 9x-7=x^2 equation:


Simplifying
9x + -7 = x2

Reorder the terms:
-7 + 9x = x2

Solving
-7 + 9x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-7 + 9x + -1x2 = 0

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

Divide each side by '-1'.
7 + -9x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -9x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -9x + x2 = 0 + -7

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

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

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -7 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + -9x + x2 = 13.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

x + -4.5 = 3.640054945 Simplifying x + -4.5 = 3.640054945 Reorder the terms: -4.5 + x = 3.640054945 Solving -4.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.640054945 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.640054945 + 4.5 x = 3.640054945 + 4.5 Combine like terms: 3.640054945 + 4.5 = 8.140054945 x = 8.140054945 Simplifying x = 8.140054945

Subproblem 2

x + -4.5 = -3.640054945 Simplifying x + -4.5 = -3.640054945 Reorder the terms: -4.5 + x = -3.640054945 Solving -4.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.640054945 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.640054945 + 4.5 x = -3.640054945 + 4.5 Combine like terms: -3.640054945 + 4.5 = 0.859945055 x = 0.859945055 Simplifying x = 0.859945055

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.140054945, 0.859945055}

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