What are the solutions to the equation (5x-2)^2-(3x+1)^2-x^2-60=0 ?

The solutions to the equation (5x-2)^2-(3x+1)^2-x^2-60=0 are x=3,x=-19/15

Find the zeros of (5x-2)^2-(3x+1)^2-x^2-60=0

The zeros of (5x-2)^2-(3x+1)^2-x^2-60=0 are x=3,x=-19/15

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(5 x - 2)^{2} - (3 x + 1)^{2} - x^{2} - 60 = 0

x = 3, x = - \frac{19}{15}

Decimal Notation

x = 3, x = - 1.26666 \dots

Solution steps

(5 x - 2)^{2} - (3 x + 1)^{2} - x^{2} - 60 = 0

Expand

(5 x - 2)^{2} - (3 x + 1)^{2} - x^{2} - 60 : 15 x^{2} - 26 x - 57

15 x^{2} - 26 x - 57 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 26 ) \pm ( - 26 ) ^{2} - 4 \cdot 15 ( - 57 )}{2 \cdot 15}

(- 26)^{2} - 4 \cdot 15 (- 57) = 64

x_{1, 2} = \frac{- ( - 26 ) \pm 64}{2 \cdot 15}

Separate the solutions

x_{1} = \frac{- ( - 26 ) + 64}{2 \cdot 15}, x_{2} = \frac{- ( - 26 ) - 64}{2 \cdot 15}

x = \frac{- ( - 26 ) + 64}{2 \cdot 15} : 3

x = \frac{- ( - 26 ) - 64}{2 \cdot 15} : - \frac{19}{15}

The solutions to the quadratic equation are:

x = 3, x = - \frac{19}{15}

x^{2} - 8 x - 11 = 0

3 x^{2} - 32 x + 64 = 0

x^{2} + 6 x + 4

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

x^{2} - 2 x - 24 = 0

What are the solutions to the equation (5x-2)^2-(3x+1)^2-x^2-60=0 ?
The solutions to the equation (5x-2)^2-(3x+1)^2-x^2-60=0 are x=3,x=-19/15
Find the zeros of (5x-2)^2-(3x+1)^2-x^2-60=0
The zeros of (5x-2)^2-(3x+1)^2-x^2-60=0 are x=3,x=-19/15