7x+1=(2x-10)(2x-10)

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Solution for 7x+1=(2x-10)(2x-10) equation: 


Simplifying
7x + 1 = (2x + -10)(2x + -10)

Reorder the terms:
1 + 7x = (2x + -10)(2x + -10)

Reorder the terms:
1 + 7x = (-10 + 2x)(2x + -10)

Reorder the terms:
1 + 7x = (-10 + 2x)(-10 + 2x)

Multiply (-10 + 2x) * (-10 + 2x)
1 + 7x = (-10(-10 + 2x) + 2x * (-10 + 2x))
1 + 7x = ((-10 * -10 + 2x * -10) + 2x * (-10 + 2x))
1 + 7x = ((100 + -20x) + 2x * (-10 + 2x))
1 + 7x = (100 + -20x + (-10 * 2x + 2x * 2x))
1 + 7x = (100 + -20x + (-20x + 4x2))

Combine like terms: -20x + -20x = -40x
1 + 7x = (100 + -40x + 4x2)

Solving
1 + 7x = 100 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
1 + -100 + 7x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 1 + -100 = -99
-99 + 7x + 40x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 7x + 40x = 47x
-99 + 47x + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Reorder the terms:
-99 + 47x + -4x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2

Combine like terms: 100 + -100 = 0
-99 + 47x + -4x2 = 0 + -40x + 40x + 4x2 + -4x2
-99 + 47x + -4x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
-99 + 47x + -4x2 = 0 + 4x2 + -4x2
-99 + 47x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-99 + 47x + -4x2 = 0

Factor a trinomial.
(-9 + x)(11 + -4x) = 0


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

Simplifying
-9 + x = 0

Solving
-9 + x = 0

Move all terms containing x to the left, all other terms to the right.

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

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

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9

Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {9, 2.75}

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