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beks73 [17]
3 years ago
5

4 + 65x52x + 7 AX =​

Mathematics
1 answer:
mars1129 [50]3 years ago
3 0

Answer:

34x+78x

Step-by-step explanation:

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Answer:

x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}

Step-by-step explanation:

<u>Given quadratic equation</u>:

y = x^2 - 6x+7

To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:

\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7

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\implies y = x^2 - 6x+9-9+7

Factor the perfect square trinomial:

\implies y=(x-3)^2-9+7

\implies y=(x-3)^2-2

To solve the quadratic, set it to zero and solve for x:

\implies (x-3)^2-2=0

\implies (x-3)^2-2+2=0+2

\implies (x-3)^2=2

\implies \sqrt{(x-3)^2}=\sqrt{2}

\implies x-3= \pm\sqrt{2}

\implies x-3+3= 3\pm\sqrt{2}

\implies x= 3\pm\sqrt{2}

Therefore, the solution to the given quadratic equation is:

x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}

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