x(2x-4)=7(x+4)

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Solution for x(2x-4)=7(x+4) equation:


Simplifying
x(2x + -4) = 7(x + 4)

Reorder the terms:
x(-4 + 2x) = 7(x + 4)
(-4 * x + 2x * x) = 7(x + 4)
(-4x + 2x2) = 7(x + 4)

Reorder the terms:
-4x + 2x2 = 7(4 + x)
-4x + 2x2 = (4 * 7 + x * 7)
-4x + 2x2 = (28 + 7x)

Solving
-4x + 2x2 = 28 + 7x

Solving for variable 'x'.

Reorder the terms:
-28 + -4x + -7x + 2x2 = 28 + 7x + -28 + -7x

Combine like terms: -4x + -7x = -11x
-28 + -11x + 2x2 = 28 + 7x + -28 + -7x

Reorder the terms:
-28 + -11x + 2x2 = 28 + -28 + 7x + -7x

Combine like terms: 28 + -28 = 0
-28 + -11x + 2x2 = 0 + 7x + -7x
-28 + -11x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-28 + -11x + 2x2 = 0

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

Divide each side by '2'.
-14 + -5.5x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -5.5x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -5.5x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -5.5x + x2 = 0 + 14
-5.5x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-5.5x + x2 = 14

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 14 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 14 + 7.5625

Combine like terms: 14 + 7.5625 = 21.5625
7.5625 + -5.5x + x2 = 21.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 21.5625

Calculate the square root of the right side: 4.643543905

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.643543905 and -4.643543905.

Subproblem 1

x + -2.75 = 4.643543905 Simplifying x + -2.75 = 4.643543905 Reorder the terms: -2.75 + x = 4.643543905 Solving -2.75 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 4.643543905 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 4.643543905 + 2.75 x = 4.643543905 + 2.75 Combine like terms: 4.643543905 + 2.75 = 7.393543905 x = 7.393543905 Simplifying x = 7.393543905

Subproblem 2

x + -2.75 = -4.643543905 Simplifying x + -2.75 = -4.643543905 Reorder the terms: -2.75 + x = -4.643543905 Solving -2.75 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -4.643543905 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -4.643543905 + 2.75 x = -4.643543905 + 2.75 Combine like terms: -4.643543905 + 2.75 = -1.893543905 x = -1.893543905 Simplifying x = -1.893543905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.393543905, -1.893543905}

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