What are the solutions to the equation (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 ?

The solutions to the equation (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 are x= 8/5 ,x= 8/29

Find the zeros of (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1

The zeros of (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 are x= 8/5 ,x= 8/29

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(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2} = + 1

x = \frac{8}{5}, x = \frac{8}{29}

Decimal Notation

x = 1.6, x = 0.27586 \dots

Solution steps

(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2} = 1

Expand

(x - 1)^{2} + ((\frac{- 5}{12}) (\frac{x + 8}{5}))^{2} : \frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9}

\frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9} = 1

Move

1

to the left side

\frac{145 x ^{2}}{144} + \frac{- 17 x + 13}{9} - 1 = 0

Write in the standard form

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

\frac{145 x ^{2}}{144} - \frac{17 x}{9} + \frac{13}{9} - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - \frac{17}{9} ) \pm ( - \frac{17}{9} ) ^{2} - 4 \cdot \frac{145}{144} ( \frac{13}{9} - 1 )}{2 \cdot \frac{145}{144}}

(- \frac{17}{9})^{2} - 4 \cdot \frac{145}{144} (\frac{13}{9} - 1) = \frac{4}{3}

x_{1, 2} = \frac{- ( - \frac{17}{9} ) \pm \frac{4}{3}}{2 \cdot \frac{145}{144}}

Separate the solutions

x_{1} = \frac{- ( - \frac{17}{9} ) + \frac{4}{3}}{2 \cdot \frac{145}{144}}, x_{2} = \frac{- ( - \frac{17}{9} ) - \frac{4}{3}}{2 \cdot \frac{145}{144}}

x = \frac{- ( - \frac{17}{9} ) + \frac{4}{3}}{2 \frac{145}{144}} : \frac{8}{5}

x = \frac{- ( - \frac{17}{9} ) - \frac{4}{3}}{2 \frac{145}{144}} : \frac{8}{29}

The solutions to the quadratic equation are:

x = \frac{8}{5}, x = \frac{8}{29}

x^{2} + 2 = 3 x

x, z = 4 - x^{2}

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

x^{2} - 6 x + 17 = 0

4 x^{2} = - x - 1

What are the solutions to the equation (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 ?
The solutions to the equation (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 are x= 8/5 ,x= 8/29
Find the zeros of (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1
The zeros of (x-1)^2+(((-5}{12})(\frac{x+8)/5))^2=+1 are x= 8/5 ,x= 8/29