2x^2-13x+47=(x-7)(x-7)

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Solution for 2x^2-13x+47=(x-7)(x-7) equation: 


Simplifying
2x2 + -13x + 47 = (x + -7)(x + -7)

Reorder the terms:
47 + -13x + 2x2 = (x + -7)(x + -7)

Reorder the terms:
47 + -13x + 2x2 = (-7 + x)(x + -7)

Reorder the terms:
47 + -13x + 2x2 = (-7 + x)(-7 + x)

Multiply (-7 + x) * (-7 + x)
47 + -13x + 2x2 = (-7(-7 + x) + x(-7 + x))
47 + -13x + 2x2 = ((-7 * -7 + x * -7) + x(-7 + x))
47 + -13x + 2x2 = ((49 + -7x) + x(-7 + x))
47 + -13x + 2x2 = (49 + -7x + (-7 * x + x * x))
47 + -13x + 2x2 = (49 + -7x + (-7x + x2))

Combine like terms: -7x + -7x = -14x
47 + -13x + 2x2 = (49 + -14x + x2)

Solving
47 + -13x + 2x2 = 49 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
47 + -49 + -13x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 47 + -49 = -2
-2 + -13x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: -13x + 14x = 1x
-2 + 1x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-2 + 1x + 1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
-2 + 1x + 1x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
-2 + 1x + 1x2 = 0 + -14x + 14x + x2 + -1x2
-2 + 1x + 1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-2 + 1x + 1x2 = 0 + x2 + -1x2
-2 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-2, 1}

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