What are the solutions to the equation (x+5)^3-x^3-15^2=50 ?

The solutions to the equation (x+5)^3-x^3-15^2=50 are x=(-5+sqrt(65))/2 ,x=-(5+sqrt(65))/2

Find the zeros of (x+5)^3-x^3-15^2=50

The zeros of (x+5)^3-x^3-15^2=50 are x=(-5+sqrt(65))/2 ,x=-(5+sqrt(65))/2

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(x + 5)^{3} - x^{3} - 1 5^{2} = 50

x = \frac{- 5 + 65}{2}, x = - \frac{5 + 65}{2}

Decimal Notation

x = 1.53112 \dots, x = - 6.53112 \dots

Solution steps

(x + 5)^{3} - x^{3} - 1 5^{2} = 50

Expand

(x + 5)^{3} - x^{3} - 1 5^{2} : 15 x^{2} + 75 x - 100

15 x^{2} + 75 x - 100 = 50

Move

50

to the left side

15 x^{2} + 75 x - 150 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 75 \pm 7 5 ^{2} - 4 \cdot 15 ( - 150 )}{2 \cdot 15}

7 5^{2} - 4 \cdot 15 (- 150) = 1565

x_{1, 2} = \frac{- 75 \pm 15 65}{2 \cdot 15}

Separate the solutions

x_{1} = \frac{- 75 + 15 65}{2 \cdot 15}, x_{2} = \frac{- 75 - 15 65}{2 \cdot 15}

x = \frac{- 75 + 15 65}{2 \cdot 15} : \frac{- 5 + 65}{2}

x = \frac{- 75 - 15 65}{2 \cdot 15} : - \frac{5 + 65}{2}

The solutions to the quadratic equation are:

x = \frac{- 5 + 65}{2}, x = - \frac{5 + 65}{2}

y^{2} - y - 3 = 0

- 5 k^{2} = - 20

0 = - x^{2} + 14 x

x^{2} - 12 x + 43

- 5 x^{2} + 94.8 x

What are the solutions to the equation (x+5)^3-x^3-15^2=50 ?
The solutions to the equation (x+5)^3-x^3-15^2=50 are x=(-5+sqrt(65))/2 ,x=-(5+sqrt(65))/2
Find the zeros of (x+5)^3-x^3-15^2=50
The zeros of (x+5)^3-x^3-15^2=50 are x=(-5+sqrt(65))/2 ,x=-(5+sqrt(65))/2