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Mashcka [7]
2 years ago
6

Find the equation that results from completing the square in the following equation.

Mathematics
2 answers:
nirvana33 [79]2 years ago
8 0
<h2>➢ <u>Answєr</u> :</h2>

\Huge{\boxed{\sf{\orange{ {(x - 6)}^2 =25}}}}

<h2>➢ <u>Explαnαtion</u> :</h2>

\displaystyle{\sf{{x}^2 - 12x + 11 = 0}}

Subtract 11 from both the sides.

\displaystyle{\sf{{x}^2 - 12x + 11 - 11 = 0 - 11}}

\implies\displaystyle{\sf{{x}^2 - 12x =  - 11}}

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b

\displaystyle{\sf{{( \frac{b}{2})}^2 = -6}}

Add the term to each side of the equation.

\implies\displaystyle{\sf{{x}^2 - 12x {-6}^2 =  - 11 {-6}^2}}

Simplify the equation.

\implies\displaystyle{\sf{{x}^2 - 12x + 36 =  25}}

Factor the perfect trinomial square into \displaystyle{\sf{(x-6)^2 }}

\large{\boxed{\sf{\red{(x-6)^2 = 25}}}}

dusya [7]2 years ago
3 0

\text{Hello there! :)}

\large\boxed{ (x-6)^{2} =25}

x^{2}  - 12x + 11 = 0\\\\\text{Complete the square by creating a perfect square trinomial:}\\\\ \text{Move 11 to the other side:}\\\\x^{2}  - 12x = -11\\\text{Divide the second term by 2 and square to complete the square.}\\\\\text{Make sure to add 36 to both sides:}\\x^2 - 12x + (36)  = -11 + (36)\\\\\text{Simplify:}\\\\(x - 6)^{2}  = -11 + 36 \\\\(x-6)^{2} = 25

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