What are the solutions to the equation (x-1)(x-3)=2x^2-9 ?

The solutions to the equation (x-1)(x-3)=2x^2-9 are x=-6,x=2

Find the zeros of (x-1)(x-3)=2x^2-9

The zeros of (x-1)(x-3)=2x^2-9 are x=-6,x=2

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(x - 1) (x - 3) = 2 x^{2} - 9

x = - 6, x = 2

Solution steps

(x - 1) (x - 3) = 2 x^{2} - 9

Expand

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

x^{2} - 4 x + 3 = 2 x^{2} - 9

Move

9

to the left side

x^{2} - 4 x + 12 = 2 x^{2}

Move

2 x^{2}

to the left side

- x^{2} - 4 x + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 ( - 1 ) \cdot 12}{2 ( - 1 )}

(- 4)^{2} - 4 (- 1) \cdot 12 = 8

x_{1, 2} = \frac{- ( - 4 ) \pm 8}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 8}{2 ( - 1 )}, x_{2} = \frac{- ( - 4 ) - 8}{2 ( - 1 )}

x = \frac{- ( - 4 ) + 8}{2 ( - 1 )} : - 6

x = \frac{- ( - 4 ) - 8}{2 ( - 1 )} : 2

The solutions to the quadratic equation are:

x = - 6, x = 2

7 x^{2} - 41 x - 6 = 0

x^{2} - 5 = - 1

x^{2} + 4 x = - 8

10 w^{2} - 13 w = 3

3.02 \cdot 1 0^{- 5} (0.0026 - x) = x^{2}

What are the solutions to the equation (x-1)(x-3)=2x^2-9 ?
The solutions to the equation (x-1)(x-3)=2x^2-9 are x=-6,x=2
Find the zeros of (x-1)(x-3)=2x^2-9
The zeros of (x-1)(x-3)=2x^2-9 are x=-6,x=2