-1x^2-7x+2=0

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Solution for -1x^2-7x+2=0 equation:


Simplifying
-1x2 + -7x + 2 = 0

Reorder the terms:
2 + -7x + -1x2 = 0

Solving
2 + -7x + -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'.
-2 + 7x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 7x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 7x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7x + x2 = 0 + 2
7x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
7x + x2 = 2

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 2 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + 7x + x2 = 14.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + 3.5 = 3.774917218 Simplifying x + 3.5 = 3.774917218 Reorder the terms: 3.5 + x = 3.774917218 Solving 3.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.774917218 + -3.5 x = 3.774917218 + -3.5 Combine like terms: 3.774917218 + -3.5 = 0.274917218 x = 0.274917218 Simplifying x = 0.274917218

Subproblem 2

x + 3.5 = -3.774917218 Simplifying x + 3.5 = -3.774917218 Reorder the terms: 3.5 + x = -3.774917218 Solving 3.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.774917218 + -3.5 x = -3.774917218 + -3.5 Combine like terms: -3.774917218 + -3.5 = -7.274917218 x = -7.274917218 Simplifying x = -7.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.274917218, -7.274917218}

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