What are the solutions to the equation x^2+2bx=a^2-b^2 ?

The solutions to the equation x^2+2bx=a^2-b^2 are x=-b+a,x=-b-a

Find the zeros of x^2+2bx=a^2-b^2

The zeros of x^2+2bx=a^2-b^2 are x=-b+a,x=-b-a

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{2} + 2 b x = a^{2} - b^{2}

x = - b + a, x = - b - a

Solution steps

x^{2} + 2 b x = a^{2} - b^{2}

Move

b^{2}

to the left side

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

Move

a^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 b \pm ( 2 b ) ^{2} - 4 \cdot 1 \cdot ( b ^{2} - a ^{2} )}{2 \cdot 1}

Simplify

(2 b)^{2} - 4 \cdot 1 \cdot (b^{2} - a^{2}) : 2 a

x_{1, 2} = \frac{- 2 b \pm 2 a}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 b + 2 a}{2 \cdot 1}, x_{2} = \frac{- 2 b - 2 a}{2 \cdot 1}

x = \frac{- 2 b + 2 a}{2 \cdot 1} : - b + a

x = \frac{- 2 b - 2 a}{2 \cdot 1} : - b - a

The solutions to the quadratic equation are:

x = - b + a, x = - b - a

5 x^{2} + 6 x - 34 = 0

4 x^{2} + 4 x = 7

5 + 2 x^{2} = 6

5 (x + 2)^{2} - 8 = 72

0 = 2 x^{2} - 3

What are the solutions to the equation x^2+2bx=a^2-b^2 ?
The solutions to the equation x^2+2bx=a^2-b^2 are x=-b+a,x=-b-a
Find the zeros of x^2+2bx=a^2-b^2
The zeros of x^2+2bx=a^2-b^2 are x=-b+a,x=-b-a