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

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


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

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

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

Multiply (7 + x) * (-4 + x)
(7(-4 + x) + x(-4 + x)) = 4
((-4 * 7 + x * 7) + x(-4 + x)) = 4
((-28 + 7x) + x(-4 + x)) = 4
(-28 + 7x + (-4 * x + x * x)) = 4
(-28 + 7x + (-4x + x2)) = 4

Combine like terms: 7x + -4x = 3x
(-28 + 3x + x2) = 4

Solving
-28 + 3x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
-28 + -4 + 3x + x2 = 4 + -4

Combine like terms: -28 + -4 = -32
-32 + 3x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-32 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 3x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 3x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3x + x2 = 0 + 32
3x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
3x + x2 = 32

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 32 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 32 + 2.25

Combine like terms: 32 + 2.25 = 34.25
2.25 + 3x + x2 = 34.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

x + 1.5 = 5.852349955 Simplifying x + 1.5 = 5.852349955 Reorder the terms: 1.5 + x = 5.852349955 Solving 1.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.852349955 + -1.5 x = 5.852349955 + -1.5 Combine like terms: 5.852349955 + -1.5 = 4.352349955 x = 4.352349955 Simplifying x = 4.352349955

Subproblem 2

x + 1.5 = -5.852349955 Simplifying x + 1.5 = -5.852349955 Reorder the terms: 1.5 + x = -5.852349955 Solving 1.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.852349955 + -1.5 x = -5.852349955 + -1.5 Combine like terms: -5.852349955 + -1.5 = -7.352349955 x = -7.352349955 Simplifying x = -7.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.352349955, -7.352349955}

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