What are the solutions to the equation (2x-3)^2-(x+5)^2=-23 ?

The solutions to the equation (2x-3)^2-(x+5)^2=-23 are x=7,x= 1/3

Find the zeros of (2x-3)^2-(x+5)^2=-23

The zeros of (2x-3)^2-(x+5)^2=-23 are x=7,x= 1/3

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(2 x - 3)^{2} - (x + 5)^{2} = - 23

x = 7, x = \frac{1}{3}

Solution steps

(2 x - 3)^{2} - (x + 5)^{2} = - 23

Expand

(2 x - 3)^{2} - (x + 5)^{2} : 3 x^{2} - 22 x - 16

3 x^{2} - 22 x - 16 = - 23

Move

23

to the left side

3 x^{2} - 22 x + 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 3 \cdot 7}{2 \cdot 3}

(- 22)^{2} - 4 \cdot 3 \cdot 7 = 20

x_{1, 2} = \frac{- ( - 22 ) \pm 20}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 22 ) + 20}{2 \cdot 3}, x_{2} = \frac{- ( - 22 ) - 20}{2 \cdot 3}

x = \frac{- ( - 22 ) + 20}{2 \cdot 3} : 7

x = \frac{- ( - 22 ) - 20}{2 \cdot 3} : \frac{1}{3}

The solutions to the quadratic equation are:

x = 7, x = \frac{1}{3}

x + 1 = 1

∣ 12 - 4 x ∣ < - 13

22 \cdot 9

81 x^{8} - 1

\frac{4 2}{2}

What are the solutions to the equation (2x-3)^2-(x+5)^2=-23 ?
The solutions to the equation (2x-3)^2-(x+5)^2=-23 are x=7,x= 1/3
Find the zeros of (2x-3)^2-(x+5)^2=-23
The zeros of (2x-3)^2-(x+5)^2=-23 are x=7,x= 1/3