What are the solutions to the equation (2x-5)^2-(x-6)^2=5 ?

The solutions to the equation (2x-5)^2-(x-6)^2=5 are x=4,x=-4/3

Find the zeros of (2x-5)^2-(x-6)^2=5

The zeros of (2x-5)^2-(x-6)^2=5 are x=4,x=-4/3

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(2 x - 5)^{2} - (x - 6)^{2} = 5

x = 4, x = - \frac{4}{3}

Decimal Notation

x = 4, x = - 1.33333 \dots

Solution steps

(2 x - 5)^{2} - (x - 6)^{2} = 5

Expand

(2 x - 5)^{2} - (x - 6)^{2} : 3 x^{2} - 8 x - 11

3 x^{2} - 8 x - 11 = 5

Move

5

to the left side

3 x^{2} - 8 x - 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 ( - 16 )}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 (- 16) = 16

x_{1, 2} = \frac{- ( - 8 ) \pm 16}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 16}{2 \cdot 3}, x_{2} = \frac{- ( - 8 ) - 16}{2 \cdot 3}

x = \frac{- ( - 8 ) + 16}{2 \cdot 3} : 4

x = \frac{- ( - 8 ) - 16}{2 \cdot 3} : - \frac{4}{3}

The solutions to the quadratic equation are:

x = 4, x = - \frac{4}{3}

3 x^{2} - 6 x + 14

2 x^{2} - 36 x = - 160

(h - 2)^{2} = 9

\frac{1}{5} x^{2} + 14 = 59

100 x^{2} + 50 x + 3 = 0

What are the solutions to the equation (2x-5)^2-(x-6)^2=5 ?
The solutions to the equation (2x-5)^2-(x-6)^2=5 are x=4,x=-4/3
Find the zeros of (2x-5)^2-(x-6)^2=5
The zeros of (2x-5)^2-(x-6)^2=5 are x=4,x=-4/3