What are the solutions to the equation ((x*(x/4+1)))/2 =60 ?

The solutions to the equation ((x*(x/4+1)))/2 =60 are x=20,x=-24

Find the zeros of ((x*(x/4+1)))/2 =60

The zeros of ((x*(x/4+1)))/2 =60 are x=20,x=-24

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\frac{( x \cdot ( \frac{x}{4} + 1 ) )}{2} = 60

x = 20, x = - 24

Solution steps

\frac{( x ( \frac{x}{4} + 1 ) )}{2} = 60

Multiply both sides by

2

x (\frac{x}{4} + 1) = 120

Expand

x (\frac{x}{4} + 1) : \frac{x ^{2}}{4} + x

\frac{x ^{2}}{4} + x = 120

Move

120

to the left side

\frac{x ^{2}}{4} + x - 120 = 0

Write in the standard form

a x^{2} + b x + c = 0

\frac{1 \cdot x ^{2}}{4} + x - 120 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot \frac{1}{4} ( - 120 )}{2 \cdot \frac{1}{4}}

1^{2} - 4 \cdot \frac{1}{4} (- 120) = 11

x_{1, 2} = \frac{- 1 \pm 11}{2 \cdot \frac{1}{4}}

Separate the solutions

x_{1} = \frac{- 1 + 11}{2 \cdot \frac{1}{4}}, x_{2} = \frac{- 1 - 11}{2 \cdot \frac{1}{4}}

x = \frac{- 1 + 11}{2 \frac{1}{4}} : 20

x = \frac{- 1 - 11}{2 \frac{1}{4}} : - 24

The solutions to the quadratic equation are:

x = 20, x = - 24

\frac{x ^{2}}{4} + 3 = 2 (x - 2)

2 a^{2} - 7 a + 3 = 0

2 = x^{2} - 12 x + 32

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

x, (m - 2) x^{2} + (n - 1) x + (p - 3) = 0

What are the solutions to the equation ((x*(x/4+1)))/2 =60 ?
The solutions to the equation ((x*(x/4+1)))/2 =60 are x=20,x=-24
Find the zeros of ((x*(x/4+1)))/2 =60
The zeros of ((x*(x/4+1)))/2 =60 are x=20,x=-24