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QUESTION 11 - 1 POINT

Use the square root property to solve the quadratic equation [tex]d^2 - 12d + 36 = 4[/tex]. If there are multiple answers, list them separated by a comma, e.g., 1, 2. If there is no solution, enter [tex]\varnothing[/tex].

Provide your answer below:

[tex]d =[/tex]



Answer :

GinnyAnswer
Certainly! Let's solve the equation [tex]\( d^2 - 12d + 36 = 4 \)[/tex] step-by-step using the square roots property.

1. First, bring the equation to standard form:

[tex]\[ d^2 - 12d + 36 - 4 = 0 \][/tex]

Which simplifies to:

[tex]\[ d^2 - 12d + 32 = 0 \][/tex]

2. Next, notice that the equation is a perfect square trinomial:

[tex]\[ (d - 6)^2 = 4 \][/tex]

3. Apply the square root property:

[tex]\[ d - 6 = \pm 2 \][/tex]

This gives us two equations to solve:

[tex]\[ \begin{cases} d - 6 = 2 \\ d - 6 = -2 \end{cases} \][/tex]

4. Solve each equation individually:

[tex]\[ \begin{cases} d - 6 = 2 & \Rightarrow d = 2 + 6 = 8 \\ d - 6 = -2 & \Rightarrow d = -2 + 6 = 4 \end{cases} \][/tex]

So, the solutions to the equation [tex]\( d^2 - 12d + 36 = 4 \)[/tex] are:

[tex]\[ d = 8, 4 \][/tex]

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