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=(11+sqrt(238))/3 ,x=(11-sqrt(238))/3

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

The zeros of (2x-3)^2-(x+5)^2=23 are x=(11+sqrt(238))/3 ,x=(11-sqrt(238))/3

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

x = \frac{11 + 238}{3}, x = \frac{11 - 238}{3}

Decimal Notation

x = 8.80908 \dots, x = - 1.47574 \dots

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 - 39 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 3 ( - 39 )}{2 \cdot 3}

(- 22)^{2} - 4 \cdot 3 (- 39) = 2238

x_{1, 2} = \frac{- ( - 22 ) \pm 2 238}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 22 ) + 2 238}{2 \cdot 3}, x_{2} = \frac{- ( - 22 ) - 2 238}{2 \cdot 3}

x = \frac{- ( - 22 ) + 2 238}{2 \cdot 3} : \frac{11 + 238}{3}

x = \frac{- ( - 22 ) - 2 238}{2 \cdot 3} : \frac{11 - 238}{3}

The solutions to the quadratic equation are:

x = \frac{11 + 238}{3}, x = \frac{11 - 238}{3}

x, 0 = x^{2} - 2 x - 3

(2 a)^{2} + a^{2} + (a - 1)^{2} = (a + 1)^{2} + (a - 2)^{2}

7 x^{2} + 30 x - 25 = 0

- 2 x^{2} - 5 x + 4 = 0

m^{2} - 5 m - 6 = 0

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=(11+sqrt(238))/3 ,x=(11-sqrt(238))/3
Find the zeros of (2x-3)^2-(x+5)^2=23
The zeros of (2x-3)^2-(x+5)^2=23 are x=(11+sqrt(238))/3 ,x=(11-sqrt(238))/3