What are the solutions to the equation 1/2 r^2-6r=2 ?

The solutions to the equation 1/2 r^2-6r=2 are r=2(3+sqrt(10)),r=2(3-sqrt(10))

Find the zeros of 1/2 r^2-6r=2

The zeros of 1/2 r^2-6r=2 are r=2(3+sqrt(10)),r=2(3-sqrt(10))

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\frac{1}{2} r^{2} - 6 r = 2

r = 2 (3 + 10), r = 2 (3 - 10)

Decimal Notation

r = 12.32455 \dots, r = - 0.32455 \dots

Solution steps

\frac{1}{2} r^{2} - 6 r = 2

Multiply both sides by

2

r^{2} - 12 r = 4

Move

4

to the left side

r^{2} - 12 r - 4 = 0

Solve with the quadratic formula

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

(- 12)^{2} - 4 \cdot 1 \cdot (- 4) = 410

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

Separate the solutions

r_{1} = \frac{- ( - 12 ) + 4 10}{2 \cdot 1}, r_{2} = \frac{- ( - 12 ) - 4 10}{2 \cdot 1}

r = \frac{- ( - 12 ) + 4 10}{2 \cdot 1} : 2 (3 + 10)

r = \frac{- ( - 12 ) - 4 10}{2 \cdot 1} : 2 (3 - 10)

The solutions to the quadratic equation are:

r = 2 (3 + 10), r = 2 (3 - 10)

b = 4 c - s^{2}

- x^{2} + 4 x = \frac{3}{2} x

- 10 q^{2} - 3 q - 9 = - 2 q

3 a^{2} - 7 a - 2 = 0

x^{2} + 6 x + 6 + 8 = 0

What are the solutions to the equation 1/2 r^2-6r=2 ?
The solutions to the equation 1/2 r^2-6r=2 are r=2(3+sqrt(10)),r=2(3-sqrt(10))
Find the zeros of 1/2 r^2-6r=2
The zeros of 1/2 r^2-6r=2 are r=2(3+sqrt(10)),r=2(3-sqrt(10))