(2x*2x)+(5x+13)*(5x+13)=(6x+8)*(6x+8)

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Solution for (2x*2x)+(5x+13)*(5x+13)=(6x+8)*(6x+8) equation:


Simplifying
(2x * 2x) + (5x + 13)(5x + 13) = (6x + 8)(6x + 8)

Reorder the terms for easier multiplication:
(2 * 2x * x) + (5x + 13)(5x + 13) = (6x + 8)(6x + 8)

Multiply 2 * 2
(4x * x) + (5x + 13)(5x + 13) = (6x + 8)(6x + 8)

Multiply x * x
(4x2) + (5x + 13)(5x + 13) = (6x + 8)(6x + 8)

Reorder the terms:
(4x2) + (13 + 5x)(5x + 13) = (6x + 8)(6x + 8)

Reorder the terms:
(4x2) + (13 + 5x)(13 + 5x) = (6x + 8)(6x + 8)

Multiply (13 + 5x) * (13 + 5x)
(4x2) + (13(13 + 5x) + 5x * (13 + 5x)) = (6x + 8)(6x + 8)
(4x2) + ((13 * 13 + 5x * 13) + 5x * (13 + 5x)) = (6x + 8)(6x + 8)
(4x2) + ((169 + 65x) + 5x * (13 + 5x)) = (6x + 8)(6x + 8)
(4x2) + (169 + 65x + (13 * 5x + 5x * 5x)) = (6x + 8)(6x + 8)
(4x2) + (169 + 65x + (65x + 25x2)) = (6x + 8)(6x + 8)

Combine like terms: 65x + 65x = 130x
(4x2) + (169 + 130x + 25x2) = (6x + 8)(6x + 8)

Reorder the terms:
169 + 130x + (4x2) + 25x2 = (6x + 8)(6x + 8)

Combine like terms: (4x2) + 25x2 = 29x2
169 + 130x + 29x2 = (6x + 8)(6x + 8)

Reorder the terms:
169 + 130x + 29x2 = (8 + 6x)(6x + 8)

Reorder the terms:
169 + 130x + 29x2 = (8 + 6x)(8 + 6x)

Multiply (8 + 6x) * (8 + 6x)
169 + 130x + 29x2 = (8(8 + 6x) + 6x * (8 + 6x))
169 + 130x + 29x2 = ((8 * 8 + 6x * 8) + 6x * (8 + 6x))
169 + 130x + 29x2 = ((64 + 48x) + 6x * (8 + 6x))
169 + 130x + 29x2 = (64 + 48x + (8 * 6x + 6x * 6x))
169 + 130x + 29x2 = (64 + 48x + (48x + 36x2))

Combine like terms: 48x + 48x = 96x
169 + 130x + 29x2 = (64 + 96x + 36x2)

Solving
169 + 130x + 29x2 = 64 + 96x + 36x2

Solving for variable 'x'.

Reorder the terms:
169 + -64 + 130x + -96x + 29x2 + -36x2 = 64 + 96x + 36x2 + -64 + -96x + -36x2

Combine like terms: 169 + -64 = 105
105 + 130x + -96x + 29x2 + -36x2 = 64 + 96x + 36x2 + -64 + -96x + -36x2

Combine like terms: 130x + -96x = 34x
105 + 34x + 29x2 + -36x2 = 64 + 96x + 36x2 + -64 + -96x + -36x2

Combine like terms: 29x2 + -36x2 = -7x2
105 + 34x + -7x2 = 64 + 96x + 36x2 + -64 + -96x + -36x2

Reorder the terms:
105 + 34x + -7x2 = 64 + -64 + 96x + -96x + 36x2 + -36x2

Combine like terms: 64 + -64 = 0
105 + 34x + -7x2 = 0 + 96x + -96x + 36x2 + -36x2
105 + 34x + -7x2 = 96x + -96x + 36x2 + -36x2

Combine like terms: 96x + -96x = 0
105 + 34x + -7x2 = 0 + 36x2 + -36x2
105 + 34x + -7x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
105 + 34x + -7x2 = 0

Factor a trinomial.
(7 + -1x)(15 + 7x) = 0

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Subproblem 2

Set the factor '(15 + 7x)' equal to zero and attempt to solve: Simplifying 15 + 7x = 0 Solving 15 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 7x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 7x = 0 + -15 7x = 0 + -15 Combine like terms: 0 + -15 = -15 7x = -15 Divide each side by '7'. x = -2.142857143 Simplifying x = -2.142857143

Solution

x = {7, -2.142857143}

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