7-x(x-4)=5(1-2x)

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Solution for 7-x(x-4)=5(1-2x) equation:


Simplifying
7 + -1x(x + -4) = 5(1 + -2x)

Reorder the terms:
7 + -1x(-4 + x) = 5(1 + -2x)
7 + (-4 * -1x + x * -1x) = 5(1 + -2x)
7 + (4x + -1x2) = 5(1 + -2x)
7 + 4x + -1x2 = (1 * 5 + -2x * 5)
7 + 4x + -1x2 = (5 + -10x)

Solving
7 + 4x + -1x2 = 5 + -10x

Solving for variable 'x'.

Reorder the terms:
7 + -5 + 4x + 10x + -1x2 = 5 + -10x + -5 + 10x

Combine like terms: 7 + -5 = 2
2 + 4x + 10x + -1x2 = 5 + -10x + -5 + 10x

Combine like terms: 4x + 10x = 14x
2 + 14x + -1x2 = 5 + -10x + -5 + 10x

Reorder the terms:
2 + 14x + -1x2 = 5 + -5 + -10x + 10x

Combine like terms: 5 + -5 = 0
2 + 14x + -1x2 = 0 + -10x + 10x
2 + 14x + -1x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
2 + 14x + -1x2 = 0

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

Divide each side by '-1'.
-2 + -14x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -14x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -14x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -14x + x2 = 0 + 2
-14x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-14x + x2 = 2

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 2 + 49

Reorder the terms:
49 + -14x + x2 = 2 + 49

Combine like terms: 2 + 49 = 51
49 + -14x + x2 = 51

Factor a perfect square on the left side:
(x + -7)(x + -7) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -7) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + -7 = 7.141428429 Simplifying x + -7 = 7.141428429 Reorder the terms: -7 + x = 7.141428429 Solving -7 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.141428429 + 7 x = 7.141428429 + 7 Combine like terms: 7.141428429 + 7 = 14.141428429 x = 14.141428429 Simplifying x = 14.141428429

Subproblem 2

x + -7 = -7.141428429 Simplifying x + -7 = -7.141428429 Reorder the terms: -7 + x = -7.141428429 Solving -7 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.141428429 + 7 x = -7.141428429 + 7 Combine like terms: -7.141428429 + 7 = -0.141428429 x = -0.141428429 Simplifying x = -0.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.141428429, -0.141428429}

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