What are the solutions to the equation 2x^2+(x-15)^2=4x+185 ?

The solutions to the equation 2x^2+(x-15)^2=4x+185 are x=10,x= 4/3

Find the zeros of 2x^2+(x-15)^2=4x+185

The zeros of 2x^2+(x-15)^2=4x+185 are x=10,x= 4/3

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2 x^{2} + (x - 15)^{2} = 4 x + 185

x = 10, x = \frac{4}{3}

Decimal Notation

x = 10, x = 1.33333 \dots

Solution steps

2 x^{2} + (x - 15)^{2} = 4 x + 185

Expand

2 x^{2} + (x - 15)^{2} : 3 x^{2} - 30 x + 225

3 x^{2} - 30 x + 225 = 4 x + 185

Move

185

to the left side

3 x^{2} - 30 x + 40 = 4 x

Move

4 x

to the left side

3 x^{2} - 34 x + 40 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 34 ) \pm ( - 34 ) ^{2} - 4 \cdot 3 \cdot 40}{2 \cdot 3}

(- 34)^{2} - 4 \cdot 3 \cdot 40 = 26

x_{1, 2} = \frac{- ( - 34 ) \pm 26}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 34 ) + 26}{2 \cdot 3}, x_{2} = \frac{- ( - 34 ) - 26}{2 \cdot 3}

x = \frac{- ( - 34 ) + 26}{2 \cdot 3} : 10

x = \frac{- ( - 34 ) - 26}{2 \cdot 3} : \frac{4}{3}

The solutions to the quadratic equation are:

x = 10, x = \frac{4}{3}

x^{2} + 24 x + 140 = 0

15 x^{2} + 12 = - 8 x

x^{2} - 3 x = 12 - 3 (x - 2)

x^{2} + 120 x + 10000 = 0

x^{2} - 2 (1 + 3 m) x + 7 (3 + 2 m) = 0

What are the solutions to the equation 2x^2+(x-15)^2=4x+185 ?
The solutions to the equation 2x^2+(x-15)^2=4x+185 are x=10,x= 4/3
Find the zeros of 2x^2+(x-15)^2=4x+185
The zeros of 2x^2+(x-15)^2=4x+185 are x=10,x= 4/3