x^2+7x-53=0

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Solution for x^2+7x-53=0 equation:


Simplifying
x2 + 7x + -53 = 0

Reorder the terms:
-53 + 7x + x2 = 0

Solving
-53 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + 7x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + 7x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + 7x + x2 = 0 + 53
7x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
7x + x2 = 53

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 = 53 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 53 + 12.25

Combine like terms: 53 + 12.25 = 65.25
12.25 + 7x + x2 = 65.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.077747211 and -8.077747211.

Subproblem 1

x + 3.5 = 8.077747211 Simplifying x + 3.5 = 8.077747211 Reorder the terms: 3.5 + x = 8.077747211 Solving 3.5 + x = 8.077747211 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 = 8.077747211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.077747211 + -3.5 x = 8.077747211 + -3.5 Combine like terms: 8.077747211 + -3.5 = 4.577747211 x = 4.577747211 Simplifying x = 4.577747211

Subproblem 2

x + 3.5 = -8.077747211 Simplifying x + 3.5 = -8.077747211 Reorder the terms: 3.5 + x = -8.077747211 Solving 3.5 + x = -8.077747211 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 = -8.077747211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.077747211 + -3.5 x = -8.077747211 + -3.5 Combine like terms: -8.077747211 + -3.5 = -11.577747211 x = -11.577747211 Simplifying x = -11.577747211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.577747211, -11.577747211}

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