What are the solutions to the equation 4.5x^2=2.5(x+0.5)^2 ?

The solutions to the equation 4.5x^2=2.5(x+0.5)^2 are x=-(-2.5+sqrt(11.25))/4 ,x=(2.5+sqrt(11.25))/4

Find the zeros of 4.5x^2=2.5(x+0.5)^2

The zeros of 4.5x^2=2.5(x+0.5)^2 are x=-(-2.5+sqrt(11.25))/4 ,x=(2.5+sqrt(11.25))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4.5 x^{2} = 2.5 (x + 0.5)^{2}

x = - \frac{- 2.5 + 11.25}{4}, x = \frac{2.5 + 11.25}{4}

Decimal Notation

x = - 0.21352 \dots, x = 1.46352 \dots

Solution steps

4.5 x^{2} = 2.5 (x + 0.5)^{2}

Expand

2.5 (x + 0.5)^{2} : 2.5 x^{2} + 2.5 x + 0.625

4.5 x^{2} = 2.5 x^{2} + 2.5 x + 0.625

Switch sides

2.5 x^{2} + 2.5 x + 0.625 = 4.5 x^{2}

Move

4.5 x^{2}

to the left side

- 2 x^{2} + 2.5 x + 0.625 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 2.5 \pm 2. 5 ^{2} - 4 ( - 2 ) \cdot 0.625}{2 ( - 2 )}

2. 5^{2} - 4 (- 2) \cdot 0.625 = 11.25

x_{1, 2} = \frac{- 2.5 \pm 11.25}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 2.5 + 11.25}{2 ( - 2 )}, x_{2} = \frac{- 2.5 - 11.25}{2 ( - 2 )}

x = \frac{- 2.5 + 11.25}{2 ( - 2 )} : - \frac{- 2.5 + 11.25}{4}

x = \frac{- 2.5 - 11.25}{2 ( - 2 )} : \frac{2.5 + 11.25}{4}

The solutions to the quadratic equation are:

x = - \frac{- 2.5 + 11.25}{4}, x = \frac{2.5 + 11.25}{4}

x^{2} + 27 = 12 x

x, x^{2} + x y - y^{2} = - 5

x, (x - 5) (3 x + 2) = 0

4 x^{2} - 2 x - 11 = 0

y = x^{2} - 3 x + 2, x

What are the solutions to the equation 4.5x^2=2.5(x+0.5)^2 ?
The solutions to the equation 4.5x^2=2.5(x+0.5)^2 are x=-(-2.5+sqrt(11.25))/4 ,x=(2.5+sqrt(11.25))/4
Find the zeros of 4.5x^2=2.5(x+0.5)^2
The zeros of 4.5x^2=2.5(x+0.5)^2 are x=-(-2.5+sqrt(11.25))/4 ,x=(2.5+sqrt(11.25))/4