What are the solutions to the equation 10=1000-10t-1/10 (100-t)^2 ?

The solutions to the equation 10=1000-10t-1/10 (100-t)^2 are t=10(5-2sqrt(6)),t=10(5+2sqrt(6))

Find the zeros of 10=1000-10t-1/10 (100-t)^2

The zeros of 10=1000-10t-1/10 (100-t)^2 are t=10(5-2sqrt(6)),t=10(5+2sqrt(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

10 = 1000 - 10 t - \frac{1}{10} (100 - t)^{2}

t = 10 (5 - 26), t = 10 (5 + 26)

Decimal Notation

t = 1.01020 \dots, t = 98.98979 \dots

Solution steps

10 = 1000 - 10 t - \frac{1}{10} (100 - t)^{2}

Multiply both sides by

10

100 = 10000 - 100 t - (100 - t)^{2}

Expand

10000 - 100 t - (100 - t)^{2} : - t^{2} + 100 t

100 = - t^{2} + 100 t

Switch sides

- t^{2} + 100 t = 100

Move

100

to the left side

- t^{2} + 100 t - 100 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 100 \pm 10 0 ^{2} - 4 ( - 1 ) ( - 100 )}{2 ( - 1 )}

10 0^{2} - 4 (- 1) (- 100) = 406

t_{1, 2} = \frac{- 100 \pm 40 6}{2 ( - 1 )}

Separate the solutions

t_{1} = \frac{- 100 + 40 6}{2 ( - 1 )}, t_{2} = \frac{- 100 - 40 6}{2 ( - 1 )}

t = \frac{- 100 + 40 6}{2 ( - 1 )} : 10 (5 - 26)

t = \frac{- 100 - 40 6}{2 ( - 1 )} : 10 (5 + 26)

The solutions to the quadratic equation are:

t = 10 (5 - 26), t = 10 (5 + 26)

a^{4} - 81

\frac{2}{( 3 + 4 ) ^{3}}

- \frac{1}{3} + 1

64 n - 6 \geq 36 n - 16

What are the solutions to the equation 10=1000-10t-1/10 (100-t)^2 ?
The solutions to the equation 10=1000-10t-1/10 (100-t)^2 are t=10(5-2sqrt(6)),t=10(5+2sqrt(6))
Find the zeros of 10=1000-10t-1/10 (100-t)^2
The zeros of 10=1000-10t-1/10 (100-t)^2 are t=10(5-2sqrt(6)),t=10(5+2sqrt(6))