(4+x)x=91

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Solution for (4+x)x=91 equation:


Simplifying
(4 + x) * x = 91

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

Solving
4x + x2 = 91

Solving for variable 'x'.

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

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

Begin completing the square.

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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