What are the solutions to the equation (-y+1)^2+y^2=11.5 ?

The solutions to the equation (-y+1)^2+y^2=11.5 are y=(1+sqrt(22))/2 ,y=(1-sqrt(22))/2

Find the zeros of (-y+1)^2+y^2=11.5

The zeros of (-y+1)^2+y^2=11.5 are y=(1+sqrt(22))/2 ,y=(1-sqrt(22))/2

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(- y + 1)^{2} + y^{2} = 11.5

y = \frac{1 + 22}{2}, y = \frac{1 - 22}{2}

Decimal Notation

y = 2.84520 \dots, y = - 1.84520 \dots

Solution steps

(- y + 1)^{2} + y^{2} = 11.5

Multiply both sides by

10

(- y + 1)^{2} \cdot 10 + y^{2} \cdot 10 = 115

Expand

(- y + 1)^{2} \cdot 10 + y^{2} \cdot 10 : 20 y^{2} - 20 y + 10

20 y^{2} - 20 y + 10 = 115

Move

115

to the left side

20 y^{2} - 20 y - 105 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 20 ( - 105 )}{2 \cdot 20}

(- 20)^{2} - 4 \cdot 20 (- 105) = 2022

y_{1, 2} = \frac{- ( - 20 ) \pm 20 22}{2 \cdot 20}

Separate the solutions

y_{1} = \frac{- ( - 20 ) + 20 22}{2 \cdot 20}, y_{2} = \frac{- ( - 20 ) - 20 22}{2 \cdot 20}

y = \frac{- ( - 20 ) + 20 22}{2 \cdot 20} : \frac{1 + 22}{2}

y = \frac{- ( - 20 ) - 20 22}{2 \cdot 20} : \frac{1 - 22}{2}

The solutions to the quadratic equation are:

y = \frac{1 + 22}{2}, y = \frac{1 - 22}{2}

r^{2} - 5 r - 24 = 0

- 0.2 x^{2} + 80 = 0.1 x^{2} + x + 40

v^{2} = - 11 v

2 x^{2} - 5 x = - 8

n^{2} - 15 n + 56 = 0

What are the solutions to the equation (-y+1)^2+y^2=11.5 ?
The solutions to the equation (-y+1)^2+y^2=11.5 are y=(1+sqrt(22))/2 ,y=(1-sqrt(22))/2
Find the zeros of (-y+1)^2+y^2=11.5
The zeros of (-y+1)^2+y^2=11.5 are y=(1+sqrt(22))/2 ,y=(1-sqrt(22))/2