x(x+7)=130

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Solution for x(x+7)=130 equation:


Simplifying
x(x + 7) = 130

Reorder the terms:
x(7 + x) = 130
(7 * x + x * x) = 130
(7x + x2) = 130

Solving
7x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 7x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 7x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 7x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 7x + x2 = 0 + 130
7x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
7x + x2 = 130

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 = 130 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 130 + 12.25

Combine like terms: 130 + 12.25 = 142.25
12.25 + 7x + x2 = 142.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + 3.5) equal to 11.926860442 and -11.926860442.

Subproblem 1

x + 3.5 = 11.926860442 Simplifying x + 3.5 = 11.926860442 Reorder the terms: 3.5 + x = 11.926860442 Solving 3.5 + x = 11.926860442 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 = 11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.926860442 + -3.5 x = 11.926860442 + -3.5 Combine like terms: 11.926860442 + -3.5 = 8.426860442 x = 8.426860442 Simplifying x = 8.426860442

Subproblem 2

x + 3.5 = -11.926860442 Simplifying x + 3.5 = -11.926860442 Reorder the terms: 3.5 + x = -11.926860442 Solving 3.5 + x = -11.926860442 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 = -11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.926860442 + -3.5 x = -11.926860442 + -3.5 Combine like terms: -11.926860442 + -3.5 = -15.426860442 x = -15.426860442 Simplifying x = -15.426860442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.426860442, -15.426860442}

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