(6+x)2=(4+x)(7+x)+10

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Solution for (6+x)2=(4+x)(7+x)+10 equation: 


Simplifying
(6 + x) * 2 = (4 + x)(7 + x) + 10

Reorder the terms for easier multiplication:
2(6 + x) = (4 + x)(7 + x) + 10
(6 * 2 + x * 2) = (4 + x)(7 + x) + 10
(12 + 2x) = (4 + x)(7 + x) + 10

Multiply (4 + x) * (7 + x)
12 + 2x = (4(7 + x) + x(7 + x)) + 10
12 + 2x = ((7 * 4 + x * 4) + x(7 + x)) + 10
12 + 2x = ((28 + 4x) + x(7 + x)) + 10
12 + 2x = (28 + 4x + (7 * x + x * x)) + 10
12 + 2x = (28 + 4x + (7x + x2)) + 10

Combine like terms: 4x + 7x = 11x
12 + 2x = (28 + 11x + x2) + 10

Reorder the terms:
12 + 2x = 28 + 10 + 11x + x2

Combine like terms: 28 + 10 = 38
12 + 2x = 38 + 11x + x2

Solving
12 + 2x = 38 + 11x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -38 + 2x + -11x + -1x2 = 38 + 11x + x2 + -38 + -11x + -1x2

Combine like terms: 12 + -38 = -26
-26 + 2x + -11x + -1x2 = 38 + 11x + x2 + -38 + -11x + -1x2

Combine like terms: 2x + -11x = -9x
-26 + -9x + -1x2 = 38 + 11x + x2 + -38 + -11x + -1x2

Reorder the terms:
-26 + -9x + -1x2 = 38 + -38 + 11x + -11x + x2 + -1x2

Combine like terms: 38 + -38 = 0
-26 + -9x + -1x2 = 0 + 11x + -11x + x2 + -1x2
-26 + -9x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
-26 + -9x + -1x2 = 0 + x2 + -1x2
-26 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-26 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(26 + 9x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(26 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
26 + 9x + x2 = 0

Solving
26 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 9x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 9x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 9x + x2 = 0 + -26
9x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
9x + x2 = -26

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -26 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -26 + 20.25

Combine like terms: -26 + 20.25 = -5.75
20.25 + 9x + x2 = -5.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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