7(7+6)=x(x+4)

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Solution for 7(7+6)=x(x+4) equation:


Simplifying
7(7 + 6) = x(x + 4)

Combine like terms: 7 + 6 = 13
7(13) = x(x + 4)

Multiply 7 * 13
91 = x(x + 4)

Reorder the terms:
91 = x(4 + x)
91 = (4 * x + x * x)
91 = (4x + x2)

Solving
91 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
91 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
91 + -4x + -1x2 = 0 + x2 + -1x2
91 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
91 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-91 + 4x + x2 = 0

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 4x + 91 + x2 = 0 + 91

Reorder the terms:
-91 + 91 + 4x + x2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 4x + x2 = 0 + 91
4x + x2 = 0 + 91

Combine like terms: 0 + 91 = 91
4x + x2 = 91

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 91 + 4

Reorder the terms:
4 + 4x + x2 = 91 + 4

Combine like terms: 91 + 4 = 95
4 + 4x + x2 = 95

Factor a perfect square on the left side:
(x + 2)(x + 2) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(x + 2) equal to 9.746794345 and -9.746794345.

Subproblem 1

x + 2 = 9.746794345 Simplifying x + 2 = 9.746794345 Reorder the terms: 2 + x = 9.746794345 Solving 2 + x = 9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.746794345 + -2 x = 9.746794345 + -2 Combine like terms: 9.746794345 + -2 = 7.746794345 x = 7.746794345 Simplifying x = 7.746794345

Subproblem 2

x + 2 = -9.746794345 Simplifying x + 2 = -9.746794345 Reorder the terms: 2 + x = -9.746794345 Solving 2 + x = -9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.746794345 + -2 x = -9.746794345 + -2 Combine like terms: -9.746794345 + -2 = -11.746794345 x = -11.746794345 Simplifying x = -11.746794345

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.746794345, -11.746794345}

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