What are the solutions to the equation 48= 1/2 x(x+4+x+8) ?

The solutions to the equation 48= 1/2 x(x+4+x+8) are x=-3+sqrt(57),x=-3-sqrt(57)

Find the zeros of 48= 1/2 x(x+4+x+8)

The zeros of 48= 1/2 x(x+4+x+8) are x=-3+sqrt(57),x=-3-sqrt(57)

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48 = \frac{1}{2} x (x + 4 + x + 8)

x = - 3 + 57, x = - 3 - 57

Decimal Notation

x = 4.54983 \dots, x = - 10.54983 \dots

Solution steps

48 = \frac{1}{2} x (x + 4 + x + 8)

Multiply both sides by

2

96 = x (2 x + 12)

Expand

x (2 x + 12) : 2 x^{2} + 12 x

96 = 2 x^{2} + 12 x

Switch sides

2 x^{2} + 12 x = 96

Move

96

to the left side

2 x^{2} + 12 x - 96 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 2 ( - 96 )}{2 \cdot 2}

1 2^{2} - 4 \cdot 2 (- 96) = 457

x_{1, 2} = \frac{- 12 \pm 4 57}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 12 + 4 57}{2 \cdot 2}, x_{2} = \frac{- 12 - 4 57}{2 \cdot 2}

x = \frac{- 12 + 4 57}{2 \cdot 2} : - 3 + 57

x = \frac{- 12 - 4 57}{2 \cdot 2} : - 3 - 57

The solutions to the quadratic equation are:

x = - 3 + 57, x = - 3 - 57

\frac{\frac{1}{q} + \frac{q}{p}}{\frac{p}{q} - \frac{1}{p}}

\frac{a + b}{6} - \frac{a - 2 b}{6}

9^{7}

3 m^{2} + 4 m - 4

9 p^{7} - 36 p^{5}

What are the solutions to the equation 48= 1/2 x(x+4+x+8) ?
The solutions to the equation 48= 1/2 x(x+4+x+8) are x=-3+sqrt(57),x=-3-sqrt(57)
Find the zeros of 48= 1/2 x(x+4+x+8)
The zeros of 48= 1/2 x(x+4+x+8) are x=-3+sqrt(57),x=-3-sqrt(57)