What are the solutions to the equation (2x-1)^2=8-x ?

The solutions to the equation (2x-1)^2=8-x are x= 7/4 ,x=-1

Find the zeros of (2x-1)^2=8-x

The zeros of (2x-1)^2=8-x are x= 7/4 ,x=-1

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(2 x - 1)^{2} = 8 - x

x = \frac{7}{4}, x = - 1

Decimal Notation

x = 1.75, x = - 1

Solution steps

(2 x - 1)^{2} = 8 - x

Expand

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

4 x^{2} - 4 x + 1 = 8 - x

Move

x

to the left side

4 x^{2} - 3 x + 1 = 8

Move

8

to the left side

4 x^{2} - 3 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 4 ( - 7 )}{2 \cdot 4}

(- 3)^{2} - 4 \cdot 4 (- 7) = 11

x_{1, 2} = \frac{- ( - 3 ) \pm 11}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 11}{2 \cdot 4}, x_{2} = \frac{- ( - 3 ) - 11}{2 \cdot 4}

x = \frac{- ( - 3 ) + 11}{2 \cdot 4} : \frac{7}{4}

x = \frac{- ( - 3 ) - 11}{2 \cdot 4} : - 1

The solutions to the quadratic equation are:

x = \frac{7}{4}, x = - 1

- 7 x < - 21

\frac{a - 2}{\frac{4}{a} - a}

- 4 x^{2} - 6 x - 1 = 0

(2 x - 3)^{2} = 8

\frac{2}{3} y - 6 = 6

What are the solutions to the equation (2x-1)^2=8-x ?
The solutions to the equation (2x-1)^2=8-x are x= 7/4 ,x=-1
Find the zeros of (2x-1)^2=8-x
The zeros of (2x-1)^2=8-x are x= 7/4 ,x=-1