What are the solutions to the equation 1/2 c^2+3c=1 ?

The solutions to the equation 1/2 c^2+3c=1 are c=-3+sqrt(11),c=-3-sqrt(11)

Find the zeros of 1/2 c^2+3c=1

The zeros of 1/2 c^2+3c=1 are c=-3+sqrt(11),c=-3-sqrt(11)

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\frac{1}{2} c^{2} + 3 c = 1

c = - 3 + 11, c = - 3 - 11

Decimal Notation

c = 0.31662 \dots, c = - 6.31662 \dots

Solution steps

\frac{1}{2} c^{2} + 3 c = 1

Multiply both sides by

2

c^{2} + 6 c = 2

Move

2

to the left side

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

Solve with the quadratic formula

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

6^{2} - 4 \cdot 1 \cdot (- 2) = 211

c_{1, 2} = \frac{- 6 \pm 2 11}{2 \cdot 1}

Separate the solutions

c_{1} = \frac{- 6 + 2 11}{2 \cdot 1}, c_{2} = \frac{- 6 - 2 11}{2 \cdot 1}

c = \frac{- 6 + 2 11}{2 \cdot 1} : - 3 + 11

c = \frac{- 6 - 2 11}{2 \cdot 1} : - 3 - 11

The solutions to the quadratic equation are:

c = - 3 + 11, c = - 3 - 11

t^{2} - t + 6 = 0

x^{2} + 2 x - 9 = 0

x, - 493 + 46 x - x^{2} = 0

x^{2} - 9.9 x - 312.5 = 0

E, S = \frac{E ^{2}}{Z}

What are the solutions to the equation 1/2 c^2+3c=1 ?
The solutions to the equation 1/2 c^2+3c=1 are c=-3+sqrt(11),c=-3-sqrt(11)
Find the zeros of 1/2 c^2+3c=1
The zeros of 1/2 c^2+3c=1 are c=-3+sqrt(11),c=-3-sqrt(11)