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

Answer from: Quest

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

Answer from: Quest

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)

= sin(7pi/6 - 2pi/6)

= sin(5pi/6)

= sin(pi - pi/6)

= sin(pi/6)

= 1/2

sin 7pi/6 - sin pi/3

= sin (pi + pi/6) - sin pi/3

= -sin pi/6 - sin pi/3