What are the solutions to the equation C=0.5x^2+15x+5000 ?

The solutions to the equation C=0.5x^2+15x+5000 are x=-15+sqrt(2C-9775),x=-sqrt(2C-9775)-15

Find the zeros of C=0.5x^2+15x+5000

The zeros of C=0.5x^2+15x+5000 are x=-15+sqrt(2C-9775),x=-sqrt(2C-9775)-15

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C = 0.5 x^{2} + 15 x + 5000

x = - 15 + 2 C - 9775, x = - 2 C - 9775 - 15

Solution steps

C = 0.5 x^{2} + 15 x + 5000

Multiply both sides by

10

C \cdot 10 = 5 x^{2} + 150 x + 50000

Switch sides

5 x^{2} + 150 x + 50000 = C \cdot 10

Move

C 10

to the left side

5 x^{2} + 150 x + 50000 - C \cdot 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 150 \pm 15 0 ^{2} - 4 \cdot 5 ( 50000 - C \cdot 10 )}{2 \cdot 5}

Simplify

15 0^{2} - 4 \cdot 5 (50000 - C \cdot 10) : 10 2 C - 9775

x_{1, 2} = \frac{- 150 \pm 10 2 C - 9775}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 150 + 10 2 C - 9775}{2 \cdot 5}, x_{2} = \frac{- 150 - 10 2 C - 9775}{2 \cdot 5}

x = \frac{- 150 + 10 2 C - 9775}{2 \cdot 5} : - 15 + 2 C - 9775

x = \frac{- 150 - 10 2 C - 9775}{2 \cdot 5} : - 2 C - 9775 - 15

The solutions to the quadratic equation are:

x = - 15 + 2 C - 9775, x = - 2 C - 9775 - 15

- 12 x - x^{2} = 0

2 x^{2} - 12 x + 1 = 15

x^{2} - \frac{x}{3} = 0

x^{2} + 10 x - 7

3 = 4 x - x^{2}

What are the solutions to the equation C=0.5x^2+15x+5000 ?
The solutions to the equation C=0.5x^2+15x+5000 are x=-15+sqrt(2C-9775),x=-sqrt(2C-9775)-15
Find the zeros of C=0.5x^2+15x+5000
The zeros of C=0.5x^2+15x+5000 are x=-15+sqrt(2C-9775),x=-sqrt(2C-9775)-15