7x+18=(-2x+3)(-2x+3)

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Solution for 7x+18=(-2x+3)(-2x+3) equation:


Simplifying
7x + 18 = (-2x + 3)(-2x + 3)

Reorder the terms:
18 + 7x = (-2x + 3)(-2x + 3)

Reorder the terms:
18 + 7x = (3 + -2x)(-2x + 3)

Reorder the terms:
18 + 7x = (3 + -2x)(3 + -2x)

Multiply (3 + -2x) * (3 + -2x)
18 + 7x = (3(3 + -2x) + -2x * (3 + -2x))
18 + 7x = ((3 * 3 + -2x * 3) + -2x * (3 + -2x))
18 + 7x = ((9 + -6x) + -2x * (3 + -2x))
18 + 7x = (9 + -6x + (3 * -2x + -2x * -2x))
18 + 7x = (9 + -6x + (-6x + 4x2))

Combine like terms: -6x + -6x = -12x
18 + 7x = (9 + -12x + 4x2)

Solving
18 + 7x = 9 + -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
18 + -9 + 7x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: 18 + -9 = 9
9 + 7x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: 7x + 12x = 19x
9 + 19x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Reorder the terms:
9 + 19x + -4x2 = 9 + -9 + -12x + 12x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
9 + 19x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2
9 + 19x + -4x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
9 + 19x + -4x2 = 0 + 4x2 + -4x2
9 + 19x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + 19x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + -4.75x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -4.75x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -4.75x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -4.75x + x2 = 0 + 2.25
-4.75x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-4.75x + x2 = 2.25

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 2.25 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 2.25 + 5.640625

Combine like terms: 2.25 + 5.640625 = 7.890625
5.640625 + -4.75x + x2 = 7.890625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 7.890625

Calculate the square root of the right side: 2.809025632

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.809025632 and -2.809025632.

Subproblem 1

x + -2.375 = 2.809025632 Simplifying x + -2.375 = 2.809025632 Reorder the terms: -2.375 + x = 2.809025632 Solving -2.375 + x = 2.809025632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.809025632 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.809025632 + 2.375 x = 2.809025632 + 2.375 Combine like terms: 2.809025632 + 2.375 = 5.184025632 x = 5.184025632 Simplifying x = 5.184025632

Subproblem 2

x + -2.375 = -2.809025632 Simplifying x + -2.375 = -2.809025632 Reorder the terms: -2.375 + x = -2.809025632 Solving -2.375 + x = -2.809025632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.809025632 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.809025632 + 2.375 x = -2.809025632 + 2.375 Combine like terms: -2.809025632 + 2.375 = -0.434025632 x = -0.434025632 Simplifying x = -0.434025632

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.184025632, -0.434025632}

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