What are the solutions to the equation ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 ?

The solutions to the equation ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 are x= 21/5 ,x=1

Find the zeros of ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1

The zeros of ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 are x= 21/5 ,x=1

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\frac{( x - 1 ) ^{2}}{16} + \frac{( x - 3 ) ^{2}}{4} = 1

x = \frac{21}{5}, x = 1

Decimal Notation

x = 4.2, x = 1

Solution steps

\frac{( x - 1 ) ^{2}}{16} + \frac{( x - 3 ) ^{2}}{4} = 1

Find Least Common Multiplier of

16, 4 : 16

Multiply by LCM=

16

\frac{( x - 1 ) ^{2}}{16} \cdot 16 + \frac{( x - 3 ) ^{2}}{4} \cdot 16 = 1 \cdot 16

Simplify

(x - 1)^{2} + 4 (x - 3)^{2} = 16

Expand

(x - 1)^{2} + 4 (x - 3)^{2} : 5 x^{2} - 26 x + 37

5 x^{2} - 26 x + 37 = 16

Move

16

to the left side

5 x^{2} - 26 x + 21 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 26 ) \pm ( - 26 ) ^{2} - 4 \cdot 5 \cdot 21}{2 \cdot 5}

(- 26)^{2} - 4 \cdot 5 \cdot 21 = 16

x_{1, 2} = \frac{- ( - 26 ) \pm 16}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 26 ) + 16}{2 \cdot 5}, x_{2} = \frac{- ( - 26 ) - 16}{2 \cdot 5}

x = \frac{- ( - 26 ) + 16}{2 \cdot 5} : \frac{21}{5}

x = \frac{- ( - 26 ) - 16}{2 \cdot 5} : 1

The solutions to the quadratic equation are:

x = \frac{21}{5}, x = 1

a, (a + b 2) \cdot (a + b 2) = 1

x^{2} + 2 = 7 x

X^{2} \cdot \frac{250}{2} + 400 \cdot (X - 100) = 8.68 \cdot 1271 \cdot (550 - X)

x^{2} + 2 = 38

2 x^{2} = 50 x

What are the solutions to the equation ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 ?
The solutions to the equation ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 are x= 21/5 ,x=1
Find the zeros of ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1
The zeros of ((x-1)^2}{16}+\frac{(x-3)^2)/4 =1 are x= 21/5 ,x=1