15x+3-2(x-1)=(7-x)(7+x)

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Solution for 15x+3-2(x-1)=(7-x)(7+x) equation:


Simplifying
15x + 3 + -2(x + -1) = (7 + -1x)(7 + x)

Reorder the terms:
15x + 3 + -2(-1 + x) = (7 + -1x)(7 + x)
15x + 3 + (-1 * -2 + x * -2) = (7 + -1x)(7 + x)
15x + 3 + (2 + -2x) = (7 + -1x)(7 + x)

Reorder the terms:
3 + 2 + 15x + -2x = (7 + -1x)(7 + x)

Combine like terms: 3 + 2 = 5
5 + 15x + -2x = (7 + -1x)(7 + x)

Combine like terms: 15x + -2x = 13x
5 + 13x = (7 + -1x)(7 + x)

Multiply (7 + -1x) * (7 + x)
5 + 13x = (7(7 + x) + -1x * (7 + x))
5 + 13x = ((7 * 7 + x * 7) + -1x * (7 + x))
5 + 13x = ((49 + 7x) + -1x * (7 + x))
5 + 13x = (49 + 7x + (7 * -1x + x * -1x))
5 + 13x = (49 + 7x + (-7x + -1x2))

Combine like terms: 7x + -7x = 0
5 + 13x = (49 + 0 + -1x2)
5 + 13x = (49 + -1x2)

Solving
5 + 13x = 49 + -1x2

Solving for variable 'x'.

Reorder the terms:
5 + -49 + 13x + x2 = 49 + -1x2 + -49 + x2

Combine like terms: 5 + -49 = -44
-44 + 13x + x2 = 49 + -1x2 + -49 + x2

Reorder the terms:
-44 + 13x + x2 = 49 + -49 + -1x2 + x2

Combine like terms: 49 + -49 = 0
-44 + 13x + x2 = 0 + -1x2 + x2
-44 + 13x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-44 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 13x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 13x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 13x + x2 = 0 + 44
13x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
13x + x2 = 44

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 44 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 44 + 42.25

Combine like terms: 44 + 42.25 = 86.25
42.25 + 13x + x2 = 86.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 86.25

Calculate the square root of the right side: 9.287087811

Break this problem into two subproblems by setting 
(x + 6.5) equal to 9.287087811 and -9.287087811.

Subproblem 1

x + 6.5 = 9.287087811 Simplifying x + 6.5 = 9.287087811 Reorder the terms: 6.5 + x = 9.287087811 Solving 6.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.287087811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.287087811 + -6.5 x = 9.287087811 + -6.5 Combine like terms: 9.287087811 + -6.5 = 2.787087811 x = 2.787087811 Simplifying x = 2.787087811

Subproblem 2

x + 6.5 = -9.287087811 Simplifying x + 6.5 = -9.287087811 Reorder the terms: 6.5 + x = -9.287087811 Solving 6.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.287087811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.287087811 + -6.5 x = -9.287087811 + -6.5 Combine like terms: -9.287087811 + -6.5 = -15.787087811 x = -15.787087811 Simplifying x = -15.787087811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.787087811, -15.787087811}

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