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

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

x=5

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

no, her answer is not correct. we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306. this is not equal to the square of the longest side ( that square being 395. answer c is correct.

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