What are the solutions to the equation (x(x+1))/2 =91 ?

The solutions to the equation (x(x+1))/2 =91 are x=13,x=-14

Find the zeros of (x(x+1))/2 =91

The zeros of (x(x+1))/2 =91 are x=13,x=-14

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\frac{x ( x + 1 )}{2} = 91

x = 13, x = - 14

Solution steps

\frac{x ( x + 1 )}{2} = 91

Multiply both sides by

2

x (x + 1) = 182

Expand

x (x + 1) : x^{2} + x

x^{2} + x = 182

Move

182

to the left side

x^{2} + x - 182 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 182 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 182) = 27

x_{1, 2} = \frac{- 1 \pm 27}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 1 + 27}{2 \cdot 1}, x_{2} = \frac{- 1 - 27}{2 \cdot 1}

x = \frac{- 1 + 27}{2 \cdot 1} : 13

x = \frac{- 1 - 27}{2 \cdot 1} : - 14

The solutions to the quadratic equation are:

x = 13, x = - 14

x^{2} - x - 3

2 x^{2} - 5 x - 3

u^{2} + 16 u

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

5 x^{2} + 2 x - 9 = 0

What are the solutions to the equation (x(x+1))/2 =91 ?
The solutions to the equation (x(x+1))/2 =91 are x=13,x=-14
Find the zeros of (x(x+1))/2 =91
The zeros of (x(x+1))/2 =91 are x=13,x=-14