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Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.

Sagot :

The roots of the given polynomials exist  [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].

What is the formula of the quadratic equation?

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0$[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]

simplifying the equation, we get

[tex]${data-answer}amp;x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]${data-answer}amp;x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]${data-answer}amp;x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and

[tex]$x=8-\sqrt{10}$[/tex].

To learn more about quadratic equations refer to:

brainly.com/question/1214333

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