What are the solutions to the equation 6p-6=p^2 ?

The solutions to the equation 6p-6=p^2 are p=3+sqrt(3),p=3-sqrt(3)

Find the zeros of 6p-6=p^2

The zeros of 6p-6=p^2 are p=3+sqrt(3),p=3-sqrt(3)

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6 p - 6 = p^{2}

p = 3 + 3, p = 3 - 3

Decimal Notation

p = 4.73205 \dots, p = 1.26794 \dots

Solution steps

6 p - 6 = p^{2}

Switch sides

p^{2} = 6 p - 6

Move

6

to the left side

p^{2} + 6 = 6 p

Move

6 p

to the left side

p^{2} + 6 - 6 p = 0

Write in the standard form

a x^{2} + b x + c = 0

p^{2} - 6 p + 6 = 0

Solve with the quadratic formula

p_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 6}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot 6 = 23

p_{1, 2} = \frac{- ( - 6 ) \pm 2 3}{2 \cdot 1}

Separate the solutions

p_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 1}, p_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 1}

p = \frac{- ( - 6 ) + 2 3}{2 \cdot 1} : 3 + 3

p = \frac{- ( - 6 ) - 2 3}{2 \cdot 1} : 3 - 3

The solutions to the quadratic equation are:

p = 3 + 3, p = 3 - 3

2 x^{2} - 9 x - 2 = - 6

\frac{( 2 x \cdot ( x - 4 ) )}{3} + \frac{x}{5} = \frac{5}{3}

\frac{x ^{2}}{6} - \frac{24}{9} = 0

4 x^{2} - 14 x - 30 = 0

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

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