What are the solutions to the equation 1/10 q^2+5=20-q/2 ?

The solutions to the equation 1/10 q^2+5=20-q/2 are q=10,q=-15

Find the zeros of 1/10 q^2+5=20-q/2

The zeros of 1/10 q^2+5=20-q/2 are q=10,q=-15

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\frac{1}{10} q^{2} + 5 = 20 - \frac{q}{2}

q = 10, q = - 15

Solution steps

\frac{1}{10} q^{2} + 5 = 20 - \frac{q}{2}

Find Least Common Multiplier of

10, 2 : 10

Multiply by LCM=

10

\frac{1}{10} q^{2} \cdot 10 + 5 \cdot 10 = 20 \cdot 10 - \frac{q}{2} \cdot 10

Simplify

q^{2} + 50 = 200 - 5 q

Move

5 q

to the left side

q^{2} + 50 + 5 q = 200

Move

200

to the left side

q^{2} + 5 q - 150 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot ( - 150 )}{2 \cdot 1}

5^{2} - 4 \cdot 1 \cdot (- 150) = 25

q_{1, 2} = \frac{- 5 \pm 25}{2 \cdot 1}

Separate the solutions

q_{1} = \frac{- 5 + 25}{2 \cdot 1}, q_{2} = \frac{- 5 - 25}{2 \cdot 1}

q = \frac{- 5 + 25}{2 \cdot 1} : 10

q = \frac{- 5 - 25}{2 \cdot 1} : - 15

The solutions to the quadratic equation are:

q = 10, q = - 15

x, x^{2} + y^{2} + z^{2} = 6 x - 4 y - 10 z

x^{2} - 3 x - 4 = 0

4.9 t^{2} + 8 t - 25 = 0

x, z^{2} = 4 + 4 (x^{2} + y^{2})

2 (x - 1)^{2} - 36 = 0

What are the solutions to the equation 1/10 q^2+5=20-q/2 ?
The solutions to the equation 1/10 q^2+5=20-q/2 are q=10,q=-15
Find the zeros of 1/10 q^2+5=20-q/2
The zeros of 1/10 q^2+5=20-q/2 are q=10,q=-15