-x^2+4x+7=0

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Solution for -x^2+4x+7=0 equation: 


Simplifying
-1x2 + 4x + 7 = 0

Reorder the terms:
7 + 4x + -1x2 = 0

Solving
7 + 4x + -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 + -4x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -4x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -4x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x + x2 = 0 + 7
-4x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-4x + x2 = 7

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 7 + 4

Reorder the terms:
4 + -4x + x2 = 7 + 4

Combine like terms: 7 + 4 = 11
4 + -4x + x2 = 11

Factor a perfect square on the left side:
(x + -2)(x + -2) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -2) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + -2 = 3.31662479

Simplifying
x + -2 = 3.31662479

Reorder the terms:
-2 + x = 3.31662479

Solving
-2 + x = 3.31662479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 3.31662479 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.31662479 + 2
x = 3.31662479 + 2

Combine like terms: 3.31662479 + 2 = 5.31662479
x = 5.31662479

Simplifying
x = 5.31662479


Subproblem 2
x + -2 = -3.31662479

Simplifying
x + -2 = -3.31662479

Reorder the terms:
-2 + x = -3.31662479

Solving
-2 + x = -3.31662479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -3.31662479 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.31662479 + 2
x = -3.31662479 + 2

Combine like terms: -3.31662479 + 2 = -1.31662479
x = -1.31662479

Simplifying
x = -1.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.31662479, -1.31662479}

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