Mathematics, 11.06.2021 05:50 kalithekittenqueen

Solve x^2-16x + 89 = 0 using the Quadratic Formula.

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Answer from: Isabelcastillox9096

$\large{ \tt{❃ \: EXPLANATION}} : \$

In solving a quadratic equation of the form ax² + bx + c = 0 by completing the square , we obtain two roots of x. Those roots can be written as $\tt{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac } }{2a} }$ where a is the coefficient of x² , b is the coefficient of x and c is the constant term. We use this formula to find the required solutions of the given quadratic equation.

$\large{ \tt{❁ \: SOLUTION}} :$

$\large{ \bf{⋆ \: {x}^{2} - 16x + 89 = 0}}$

$\large{ \bf{↦{x}^{2} + ( - 16x) + 89 = 0 }}$

Here , a = 1 , b = -16 and c = 89

$\large{ \tt{⇢x = \frac{ - b \: ± \sqrt{ {b}^{2} - 4ac} }{2a} } = \frac{ - 16 \:± \: \sqrt{ {( - 16)}^{2} - 4 \times 1 \times 89} }{2 \times 1} = \frac{ - 16 \: ± \: \sqrt{256 - 356} }{2} = \frac{ - 16 \: ± \: \sqrt{ \underline{- 100}} }{2}}$

The square root of negative number does not exist in the set of real numbers. So, This cannot be further solved!

$\large{ \boxed{ \boxed{ \tt{ ⇝\: OUR \: FINAL \: ANSWER : \boxed{ \underline { \tt{{NO \: REAL \: SOLUTIONS}}}}}}} \: ✔}$

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Answer from: emily41950

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Problem:Solve it using quadratic formula.

$\quad\quad\quad\quad\tt{ {x}^{2} - 16x + 89 = 0}$

The standard form of:

$\quad\quad\quad\quad\tt{ {a}^{2} + bx + c = 0}$

Given that:a = 1b = - 16c = 89This has a discriminant ∆ given by the formula:

$\quad\quad\quad\quad\tt{∆ = {b}^{2} - 4ac}$

$\quad\quad\quad\quad\tt{∆ = {( - 16)}^{2} - 4(1)(89)}$

$\quad\quad\quad\quad\tt{∆ = {256 - 356}}$

$\quad\quad\quad\quad\tt{∆ = { - 100}}$

$\quad\quad\quad\quad\tt{∆ = { - 10}^{2} }$

Since ∆ < 0 this equation has no real solutions, only complex ones.One way of finding the solutions is using the quadratic formula:

$\quad\quad\quad\quad\tt{x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} }$

$\quad\quad\quad\quad\tt{x = \frac{ - b \: ± \: \sqrt{∆} }{2a} }$

$\quad\quad\quad\quad\tt{x = \frac{ 16 \: ± \: \sqrt{ - 1 00 } }{2} }$

$\quad\quad\quad\quad\tt{x = \frac{ 16 \: ± \: \sqrt{ - 1 00 i} }{2} }$

$\quad\quad\quad\quad\tt{x = \frac{ 16 \: ± \: 1 0 i }{2} }$

$\quad\quad\quad\quad\tt{x = 8 \: ± \: 5 i}$

So the final answer is:

$\quad\quad\quad\quad \boxed{ \boxed{\tt{ \color{magenta}x=8 \: ± \: 5 i}}}$

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✍︎ C.Rose❀

Solve x^2-16x + 89 = 0 using the Quadratic Formula.

Answer from: Quest

9/12 is the answer because 3/4 times 3 each is 9/12

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

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Solve x^2-16x + 89 = 0 using the Quadratic Formula....

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