What are the solutions to the equation 2x(x-6)=10 ?

The solutions to the equation 2x(x-6)=10 are x=3+sqrt(14),x=3-sqrt(14)

Find the zeros of 2x(x-6)=10

The zeros of 2x(x-6)=10 are x=3+sqrt(14),x=3-sqrt(14)

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2 x (x - 6) = 10

x = 3 + 14, x = 3 - 14

Decimal Notation

x = 6.74165 \dots, x = - 0.74165 \dots

Solution steps

2 x (x - 6) = 10

Expand

2 x (x - 6) : 2 x^{2} - 12 x

2 x^{2} - 12 x = 10

Move

10

to the left side

2 x^{2} - 12 x - 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 2 ( - 10 )}{2 \cdot 2}

(- 12)^{2} - 4 \cdot 2 (- 10) = 414

x_{1, 2} = \frac{- ( - 12 ) \pm 4 14}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 4 14}{2 \cdot 2}, x_{2} = \frac{- ( - 12 ) - 4 14}{2 \cdot 2}

x = \frac{- ( - 12 ) + 4 14}{2 \cdot 2} : 3 + 14

x = \frac{- ( - 12 ) - 4 14}{2 \cdot 2} : 3 - 14

The solutions to the quadratic equation are:

x = 3 + 14, x = 3 - 14

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

x^{2} + 24 x - 144 = 0

2 x = 4 x^{2} - 5 x + 50

v^{2} + 10 v + 16 = 0

4 x^{2} - 5 x - 21 = 0

What are the solutions to the equation 2x(x-6)=10 ?
The solutions to the equation 2x(x-6)=10 are x=3+sqrt(14),x=3-sqrt(14)
Find the zeros of 2x(x-6)=10
The zeros of 2x(x-6)=10 are x=3+sqrt(14),x=3-sqrt(14)