(x+1)(x-4)=x+7

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Solution for (x+1)(x-4)=x+7 equation:


Simplifying
(x + 1)(x + -4) = x + 7

Reorder the terms:
(1 + x)(x + -4) = x + 7

Reorder the terms:
(1 + x)(-4 + x) = x + 7

Multiply (1 + x) * (-4 + x)
(1(-4 + x) + x(-4 + x)) = x + 7
((-4 * 1 + x * 1) + x(-4 + x)) = x + 7
((-4 + 1x) + x(-4 + x)) = x + 7
(-4 + 1x + (-4 * x + x * x)) = x + 7
(-4 + 1x + (-4x + x2)) = x + 7

Combine like terms: 1x + -4x = -3x
(-4 + -3x + x2) = x + 7

Reorder the terms:
-4 + -3x + x2 = 7 + x

Solving
-4 + -3x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-4 + -7 + -3x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -4 + -7 = -11
-11 + -3x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -3x + -1x = -4x
-11 + -4x + x2 = 7 + x + -7 + -1x

Reorder the terms:
-11 + -4x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-11 + -4x + x2 = 0 + x + -1x
-11 + -4x + x2 = x + -1x

Combine like terms: x + -1x = 0
-11 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -4x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x + x2 = 0 + 11
-4x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4x + x2 = 11

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 = 11 + 4

Reorder the terms:
4 + -4x + x2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4x + x2 = 15

Factor a perfect square on the left side:
(x + -2)(x + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -2) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + -2 = 3.872983346 Simplifying x + -2 = 3.872983346 Reorder the terms: -2 + x = 3.872983346 Solving -2 + x = 3.872983346 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 = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.872983346 + 2 x = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 x = 5.872983346 Simplifying x = 5.872983346

Subproblem 2

x + -2 = -3.872983346 Simplifying x + -2 = -3.872983346 Reorder the terms: -2 + x = -3.872983346 Solving -2 + x = -3.872983346 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 = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.872983346 + 2 x = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 x = -1.872983346 Simplifying x = -1.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.872983346, -1.872983346}

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