Solve using perfect square factoring patterns.

\[ x^2 - 12x + 36 = 4 \]

the correct solutions to the equation x 2 − 12 x + 36 = 4 are ( x = 6 ) and ( x = 6 ).
Sure, let's solve the quadratic equation x 2 − 12 x + 36 = 4 using perfect square factoring patterns. Here are the steps:

Subtract 4 from both sides of the equation to move all terms to one side:

x 2 − 12 x + 32 = 0

Identify if the quadratic expression can be factored using perfect square factoring patterns. In this case, we notice that x 2 − 12 x + 32 can be factored into a perfect square since the coefficient of the linear term (-12x) is twice the square root of the constant term (32).

Now, let's factor the quadratic expression:

Rewrite the quadratic expression as a perfect square trinomial:

( x − 6 ) 2 = 0

Solve for x by taking the square root of both sides to eliminate the squared term:

x − 6 = 0 or x − 6 = 0

Solve for x in each equation:

x = 6 or x = 6
The solutions to the equation x 2 − 12 x + 36 = 4 are x = 6 and x = 6 .[/tex]
To solve the quadratic equation[tex] x 2 − 12 x + 36 = 4 , we first subtracted 4 from both sides to rearrange the equation into the standard quadratic form x 2 − 12 x + 32 = 0 . Then, we recognized that this quadratic expression can be factored into a perfect square trinomial because the coefficient of the linear term (-12x) is twice the square root of the constant term (32).
Factoring x 2 − 12 x + 32 yields ( x − 6 ) 2 = 0 ,[/tex] which we can solve by taking the square root of both sides. This results in ( x - 6 = 0 ), leading to the solutions ( x = 6 ) and ( x = 6).
Therefore, the correct solutions to the equation[tex] x 2 − 12 x + 36 = 4 are ( x = 6 ) and ( x = 6 ).
complete question
'Solve using perfect square factoring patterns.
x^2 – 12x + 36 = 4'

Answered by shellshiyaira | 2024-06-24

The quadratic equation x² - 12x + 36 = 4 does not directly factor into a perfect square. After simplifying to x² - 12x + 32 = 0, it can be factored normally to find the solutions x = 4 and x = 8.
To solve the equation x² - 12x + 36 = 4 using perfect square factoring patterns, we first move the constant term on the right side to the left side of the equation to set it equal to zero:
x² - 12x + 36 - 4 = 0
Now, we have:
x² - 12x + 32 = 0
We observe that the left side of the equation does not factor into a perfect square as is, so this equation cannot be solved using the method of perfect square factoring patterns directly.
If we attempt to factor normally:
(x - 4)(x - 8) = 0
Setting each factor equal to zero gives us the solutions:
x = 4 or x = 8

Answered by ToddBoyce | 2024-06-24

To solve the equation x 2 − 12 x + 36 = 4 , we rearranged it to x 2 − 12 x + 32 = 0 and recognized it as a perfect square ( x − 6 ) 2 = 4 . This allows us to find that the solutions are x = 8 and x = 4 .
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Answered by shellshiyaira | 2024-12-01