-x^2+9x+7=0

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Solution for -x^2+9x+7=0 equation:


Simplifying
-1x2 + 9x + 7 = 0

Reorder the terms:
7 + 9x + -1x2 = 0

Solving
7 + 9x + -1x2 = 0

Solving for variable 'x'.

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 = 27.25
20.25 + -9x + x2 = 27.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + -4.5 = 5.220153254 Simplifying x + -4.5 = 5.220153254 Reorder the terms: -4.5 + x = 5.220153254 Solving -4.5 + x = 5.220153254 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 = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.220153254 + 4.5 x = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 x = 9.720153254 Simplifying x = 9.720153254

Subproblem 2

x + -4.5 = -5.220153254 Simplifying x + -4.5 = -5.220153254 Reorder the terms: -4.5 + x = -5.220153254 Solving -4.5 + x = -5.220153254 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 = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.220153254 + 4.5 x = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 x = -0.720153254 Simplifying x = -0.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.720153254, -0.720153254}

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