x+x^2+-7x=77

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Solution for x+x^2+-7x=77 equation:


Simplifying
x + x2 + -7x = 77

Reorder the terms:
x + -7x + x2 = 77

Combine like terms: x + -7x = -6x
-6x + x2 = 77

Solving
-6x + x2 = 77

Solving for variable 'x'.

Reorder the terms:
-77 + -6x + x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + -6x + 77 + x2 = 0 + 77

Reorder the terms:
-77 + 77 + -6x + x2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + -6x + x2 = 0 + 77
-6x + x2 = 0 + 77

Combine like terms: 0 + 77 = 77
-6x + x2 = 77

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 77 + 9

Reorder the terms:
9 + -6x + x2 = 77 + 9

Combine like terms: 77 + 9 = 86
9 + -6x + x2 = 86

Factor a perfect square on the left side:
(x + -3)(x + -3) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -3) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -3 = 9.273618495 Simplifying x + -3 = 9.273618495 Reorder the terms: -3 + x = 9.273618495 Solving -3 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.273618495 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.273618495 + 3 x = 9.273618495 + 3 Combine like terms: 9.273618495 + 3 = 12.273618495 x = 12.273618495 Simplifying x = 12.273618495

Subproblem 2

x + -3 = -9.273618495 Simplifying x + -3 = -9.273618495 Reorder the terms: -3 + x = -9.273618495 Solving -3 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.273618495 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.273618495 + 3 x = -9.273618495 + 3 Combine like terms: -9.273618495 + 3 = -6.273618495 x = -6.273618495 Simplifying x = -6.273618495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.273618495, -6.273618495}

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