What are the solutions to the equation (5x)^2+(5x+5)^2=(5x+10)^2 ?

The solutions to the equation (5x)^2+(5x+5)^2=(5x+10)^2 are x=3,x=-1

Find the zeros of (5x)^2+(5x+5)^2=(5x+10)^2

The zeros of (5x)^2+(5x+5)^2=(5x+10)^2 are x=3,x=-1

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(5 x)^{2} + (5 x + 5)^{2} = (5 x + 10)^{2}

x = 3, x = - 1

Solution steps

(5 x)^{2} + (5 x + 5)^{2} = (5 x + 10)^{2}

Expand

(5 x)^{2} + (5 x + 5)^{2} : 50 x^{2} + 50 x + 25

Expand

(5 x + 10)^{2} : 25 x^{2} + 100 x + 100

50 x^{2} + 50 x + 25 = 25 x^{2} + 100 x + 100

Move

100

to the left side

50 x^{2} + 50 x - 75 = 25 x^{2} + 100 x

Move

100 x

to the left side

50 x^{2} - 50 x - 75 = 25 x^{2}

Move

25 x^{2}

to the left side

25 x^{2} - 50 x - 75 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 50 ) \pm ( - 50 ) ^{2} - 4 \cdot 25 ( - 75 )}{2 \cdot 25}

(- 50)^{2} - 4 \cdot 25 (- 75) = 100

x_{1, 2} = \frac{- ( - 50 ) \pm 100}{2 \cdot 25}

Separate the solutions

x_{1} = \frac{- ( - 50 ) + 100}{2 \cdot 25}, x_{2} = \frac{- ( - 50 ) - 100}{2 \cdot 25}

x = \frac{- ( - 50 ) + 100}{2 \cdot 25} : 3

x = \frac{- ( - 50 ) - 100}{2 \cdot 25} : - 1

The solutions to the quadratic equation are:

x = 3, x = - 1

5^{x + 2} - 5^{x - 1}

0.0 1^{2}

5 x^{2} + 20 x

8 d - d - 4 d - 8 = 5 d

3 a^{2} + 7 a

What are the solutions to the equation (5x)^2+(5x+5)^2=(5x+10)^2 ?
The solutions to the equation (5x)^2+(5x+5)^2=(5x+10)^2 are x=3,x=-1
Find the zeros of (5x)^2+(5x+5)^2=(5x+10)^2
The zeros of (5x)^2+(5x+5)^2=(5x+10)^2 are x=3,x=-1