What are the solutions to the equation (X+3)^2-(X-1)^2=X^2 ?

The solutions to the equation (X+3)^2-(X-1)^2=X^2 are X=2(2+sqrt(6)),X=2(2-sqrt(6))

Find the zeros of (X+3)^2-(X-1)^2=X^2

The zeros of (X+3)^2-(X-1)^2=X^2 are X=2(2+sqrt(6)),X=2(2-sqrt(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(X + 3)^{2} - (X - 1)^{2} = X^{2}

X = 2 (2 + 6), X = 2 (2 - 6)

Decimal Notation

X = 8.89897 \dots, X = - 0.89897 \dots

Solution steps

(X + 3)^{2} - (X - 1)^{2} = X^{2}

Expand

(X + 3)^{2} - (X - 1)^{2} : 8 X + 8

8 X + 8 = X^{2}

Switch sides

X^{2} = 8 X + 8

Move

8

to the left side

X^{2} - 8 = 8 X

Move

8 X

to the left side

X^{2} - 8 - 8 X = 0

Write in the standard form

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

X^{2} - 8 X - 8 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot (- 8) = 46

X_{1, 2} = \frac{- ( - 8 ) \pm 4 6}{2 \cdot 1}

Separate the solutions

X_{1} = \frac{- ( - 8 ) + 4 6}{2 \cdot 1}, X_{2} = \frac{- ( - 8 ) - 4 6}{2 \cdot 1}

X = \frac{- ( - 8 ) + 4 6}{2 \cdot 1} : 2 (2 + 6)

X = \frac{- ( - 8 ) - 4 6}{2 \cdot 1} : 2 (2 - 6)

The solutions to the quadratic equation are:

X = 2 (2 + 6), X = 2 (2 - 6)

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

15 x^{2} - 38 x - 32 = 0

3 x^{2} - 4 x + 10 = 0

x^{2} + 101.9 x + 2 \cdot 1 0^{5} = 0

2 x^{2} - 8 x + 3 = 0

What are the solutions to the equation (X+3)^2-(X-1)^2=X^2 ?
The solutions to the equation (X+3)^2-(X-1)^2=X^2 are X=2(2+sqrt(6)),X=2(2-sqrt(6))
Find the zeros of (X+3)^2-(X-1)^2=X^2
The zeros of (X+3)^2-(X-1)^2=X^2 are X=2(2+sqrt(6)),X=2(2-sqrt(6))