What are the solutions to the equation 625^2=x^2+(x/2+75)^2 ?

The solutions to the equation 625^2=x^2+(x/2+75)^2 are x=10(sqrt(3089)-3),x=-10(3+sqrt(3089))

Find the zeros of 625^2=x^2+(x/2+75)^2

The zeros of 625^2=x^2+(x/2+75)^2 are x=10(sqrt(3089)-3),x=-10(3+sqrt(3089))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

62 5^{2} = x^{2} + (\frac{x}{2} + 75)^{2}

x = 10 (3089 - 3), x = - 10 (3 + 3089)

Decimal Notation

x = 525.78772 \dots, x = - 585.78772 \dots

Solution steps

62 5^{2} = x^{2} + (\frac{x}{2} + 75)^{2}

Expand

62 5^{2} : 390625

Expand

x^{2} + (\frac{x}{2} + 75)^{2} : \frac{5 x ^{2}}{4} + 75 x + 5625

390625 = \frac{5 x ^{2}}{4} + 75 x + 5625

Switch sides

\frac{5 x ^{2}}{4} + 75 x + 5625 = 390625

Move

390625

to the left side

\frac{5 x ^{2}}{4} + 75 x - 385000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 75 \pm 7 5 ^{2} - 4 \cdot \frac{5}{4} ( - 385000 )}{2 \cdot \frac{5}{4}}

7 5^{2} - 4 \cdot \frac{5}{4} (- 385000) = 253089

x_{1, 2} = \frac{- 75 \pm 25 3089}{2 \cdot \frac{5}{4}}

Separate the solutions

x_{1} = \frac{- 75 + 25 3089}{2 \cdot \frac{5}{4}}, x_{2} = \frac{- 75 - 25 3089}{2 \cdot \frac{5}{4}}

x = \frac{- 75 + 25 3089}{2 \frac{5}{4}} : 10 (3089 - 3)

x = \frac{- 75 - 25 3089}{2 \frac{5}{4}} : - 10 (3 + 3089)

The solutions to the quadratic equation are:

x = 10 (3089 - 3), x = - 10 (3 + 3089)

25 = - 10 x - x^{2}

\frac{x ^{2}}{20} + 8 = 15

18 x^{2} - 3 x - 1 = 0

0 = 6 x^{2} - 6 x

7 + 8 x^{2} = 4 x

What are the solutions to the equation 625^2=x^2+(x/2+75)^2 ?
The solutions to the equation 625^2=x^2+(x/2+75)^2 are x=10(sqrt(3089)-3),x=-10(3+sqrt(3089))
Find the zeros of 625^2=x^2+(x/2+75)^2
The zeros of 625^2=x^2+(x/2+75)^2 are x=10(sqrt(3089)-3),x=-10(3+sqrt(3089))