7-5x-x^2=0

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Solution for 7-5x-x^2=0 equation:


Simplifying
7 + -5x + -1x2 = 0

Solving
7 + -5x + -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 + 5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5x + x2 = 0 + 7
5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
5x + x2 = 7

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 7 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + 5x + x2 = 13.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

x + 2.5 = 3.640054945 Simplifying x + 2.5 = 3.640054945 Reorder the terms: 2.5 + x = 3.640054945 Solving 2.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.640054945 + -2.5 x = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 x = 1.140054945 Simplifying x = 1.140054945

Subproblem 2

x + 2.5 = -3.640054945 Simplifying x + 2.5 = -3.640054945 Reorder the terms: 2.5 + x = -3.640054945 Solving 2.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.640054945 + -2.5 x = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 x = -6.140054945 Simplifying x = -6.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.140054945, -6.140054945}

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