Solve 5-left(x-4right)^2 | Microsoft Math Solver

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Evaluate

- (x - 4)^{2} + 5

Solution Steps

5 - (x - 4)^{2}

Use binomial theorem

(a - b)^{2} = a^{2} - 2 a b + b^{2}

to expand

(x - 4)^{2}

5 - (x^{2} - 8 x + 16)

To find the opposite of

x^{2} - 8 x + 16

, find the opposite of each term.

5 - x^{2} + 8 x - 16

Subtract

16

from

5

to get

- 11

- 11 - x^{2} + 8 x

Expand

- x^{2} + 8 x - 11

Solution Steps

5 - (x - 4)^{2}

Use binomial theorem

(a - b)^{2} = a^{2} - 2 a b + b^{2}

to expand

(x - 4)^{2}

5 - (x^{2} - 8 x + 16)

To find the opposite of

x^{2} - 8 x + 16

, find the opposite of each term.

5 - x^{2} + 8 x - 16

Subtract

16

from

5

to get

- 11

- 11 - x^{2} + 8 x

Factor

- (x - (4 - 5)) (x - (5 + 4))

Steps Using the Quadratic Formula

5 - (x - 4)^{2}

Use binomial theorem

(a - b)^{2} = a^{2} - 2 a b + b^{2}

to expand

(x - 4)^{2}

f a c t o r (5 - (x^{2} - 8 x + 16))

To find the opposite of

x^{2} - 8 x + 16

, find the opposite of each term.

f a c t o r (5 - x^{2} + 8 x - 16)

Subtract

16

from

5

to get

- 11

f a c t o r (- 11 - x^{2} + 8 x)

Quadratic polynomial can be factored using the transformation

a x^{2} + b x + c = a (x - x_{1}) (x - x_{2})

, where

x_{1}

and

x_{2}

are the solutions of the quadratic equation

a x^{2} + b x + c = 0

- x^{2} + 8 x - 11 = 0

All equations of the form

a x^{2} + b x + c = 0

can be solved using the quadratic formula:

\frac{- b \pm b ^{2} - 4 a c}{2 a}

. The quadratic formula gives two solutions, one when

\pm

is addition and one when it is subtraction.

x = \frac{- 8 \pm 8 ^{2} - 4 ( - 1 ) ( - 1 1 )}{2 ( - 1 )}

Square

8

x = \frac{- 8 \pm 6 4 - 4 ( - 1 ) ( - 1 1 )}{2 ( - 1 )}

Multiply

- 4

times

- 1

x = \frac{- 8 \pm 6 4 + 4 ( - 1 1 )}{2 ( - 1 )}

Multiply

4

times

- 11

x = \frac{- 8 \pm 6 4 - 4 4}{2 ( - 1 )}

Add

64

- 44

x = \frac{- 8 \pm 2 0}{2 ( - 1 )}

Take the square root of

20

x = \frac{- 8 \pm 2 5}{2 ( - 1 )}

Multiply

2

times

- 1

x = \frac{- 8 \pm 2 5}{- 2}

Now solve the equation

x = \frac{- 8 \pm 2 5}{- 2}

when

\pm

is plus. Add

- 8

25 \approx 4.472135955

x = \frac{2 5 - 8}{- 2}

Divide

- 8 + 25 \approx - 3.527864045

- 2

x = 4 - 5

Now solve the equation

x = \frac{- 8 \pm 2 5}{- 2}

when

\pm

is minus. Subtract

25 \approx 4.472135955

from

- 8

x = \frac{- 2 5 - 8}{- 2}

Divide

- 8 - 25 \approx - 12.472135955

- 2

x = 5 + 4

Factor the original expression using

a x^{2} + b x + c = a (x - x_{1}) (x - x_{2})

. Substitute

4 - 5 \approx 1.763932023

for

x_{1}

and

4 + 5 \approx 6.236067977

for

x_{2}

- x^{2} + 8 x - 11 = - (x - (4 - 5)) (x - (5 + 4))

Graph

Quiz

Polynomial

10 problems similar to:

5 - (x - 4)^{2}

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Similar Problems from Web Search

How do you expand

(5 x - 4)^{2}

https://socratic.org/questions/how-do-you-expand-5x-4-2

(5 x - 4)^{2} = 25 x^{2} - 40 x + 16

Explanation: To expand this polynomial I used the formula:

(a - b)^{2} = a^{2} - 2 a b + b^{2}

...

(x - 4)^{2} = 0

https://www.tiger-algebra.com/drill/(x-4)~2=0/

(x-4)2=0 One solution was found : x = 4 Step by step solution : Step 1 :Equation at the end of step 1 : (x - 4)2 = 0 Step 2 :Solving a Single Variable Equation : ...

(x - 4)^{2} = 1

https://www.tiger-algebra.com/drill/(x-4)~2=1/

(x-4)2=1 Two solutions were found : x = 5 x = 3 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ...

(x - 4)^{2} = 30

https://www.tiger-algebra.com/drill/(x-4)~2=30/

(x-4)2=30 Two solutions were found : x =(8-√120)/2=4-√ 30 = -1.477 x =(8+√120)/2=4+√ 30 = 9.477 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from ...

(x - 4)^{2} = 36

http://www.tiger-algebra.com/drill/(x-4)~2=36/

(x-4)2=36 Two solutions were found : x = 10 x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ...

4^{2 x} = 16

, how do we solve for x?

https://socratic.org/questions/in-4-2x-16-how-do-we-solve-for-x

(x = 1)

Explanation: Since

(XXX) 16 = 4^{2}

4^{2 x} = 16

implies

4^{2 x} = 4^{2}

...

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5-\left(x^{2}-8x+16\right)

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

5-x^{2}+8x-16

To find the opposite of x^{2}-8x+16, find the opposite of each term.

-11-x^{2}+8x

Subtract 16 from 5 to get -11.

5-\left(x^{2}-8x+16\right)

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

5-x^{2}+8x-16

To find the opposite of x^{2}-8x+16, find the opposite of each term.

-11-x^{2}+8x

Subtract 16 from 5 to get -11.

factor(5-\left(x^{2}-8x+16\right))

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

factor(5-x^{2}+8x-16)

To find the opposite of x^{2}-8x+16, find the opposite of each term.

factor(-11-x^{2}+8x)

Subtract 16 from 5 to get -11.

-x^{2}+8x-11=0

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)\left(-11\right)}}{2\left(-1\right)}

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=\frac{-8±\sqrt{64-4\left(-1\right)\left(-11\right)}}{2\left(-1\right)}

Square 8.

x=\frac{-8±\sqrt{64+4\left(-11\right)}}{2\left(-1\right)}

Multiply -4 times -1.

x=\frac{-8±\sqrt{64-44}}{2\left(-1\right)}

Multiply 4 times -11.

x=\frac{-8±\sqrt{20}}{2\left(-1\right)}

Add 64 to -44.

x=\frac{-8±2\sqrt{5}}{2\left(-1\right)}

Take the square root of 20.

x=\frac{-8±2\sqrt{5}}{-2}

Multiply 2 times -1.

x=\frac{2\sqrt{5}-8}{-2}

Now solve the equation x=\frac{-8±2\sqrt{5}}{-2} when ± is plus. Add -8 to 2\sqrt{5}\approx 4.472135955.

x=4-\sqrt{5}

Divide -8+2\sqrt{5}\approx -3.527864045 by -2.

x=\frac{-2\sqrt{5}-8}{-2}

Now solve the equation x=\frac{-8±2\sqrt{5}}{-2} when ± is minus. Subtract 2\sqrt{5}\approx 4.472135955 from -8.

x=\sqrt{5}+4

Divide -8-2\sqrt{5}\approx -12.472135955 by -2.

-x^{2}+8x-11=-\left(x-\left(4-\sqrt{5}\right)\right)\left(x-\left(\sqrt{5}+4\right)\right)

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4-\sqrt{5}\approx 1.763932023 for x_{1} and 4+\sqrt{5}\approx 6.236067977 for x_{2}.

Examples

Quadratic equation