What are the solutions to the equation 6.5=((x+x^2+5x))/2 ?

The solutions to the equation 6.5=((x+x^2+5x))/2 are x=-3+sqrt(22),x=-3-sqrt(22)

Find the zeros of 6.5=((x+x^2+5x))/2

The zeros of 6.5=((x+x^2+5x))/2 are x=-3+sqrt(22),x=-3-sqrt(22)

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6.5 = \frac{( x + x ^{2} + 5 x )}{2}

x = - 3 + 22, x = - 3 - 22

Decimal Notation

x = 1.69041 \dots, x = - 7.69041 \dots

Solution steps

6.5 = \frac{( x + x ^{2} + 5 x )}{2}

Multiply both sides by

10

65 = 5 (x^{2} + 6 x)

Expand

5 (x^{2} + 6 x) : 5 x^{2} + 30 x

65 = 5 x^{2} + 30 x

Switch sides

5 x^{2} + 30 x = 65

Move

65

to the left side

5 x^{2} + 30 x - 65 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 30 \pm 3 0 ^{2} - 4 \cdot 5 ( - 65 )}{2 \cdot 5}

3 0^{2} - 4 \cdot 5 (- 65) = 1022

x_{1, 2} = \frac{- 30 \pm 10 22}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 30 + 10 22}{2 \cdot 5}, x_{2} = \frac{- 30 - 10 22}{2 \cdot 5}

x = \frac{- 30 + 10 22}{2 \cdot 5} : - 3 + 22

x = \frac{- 30 - 10 22}{2 \cdot 5} : - 3 - 22

The solutions to the quadratic equation are:

x = - 3 + 22, x = - 3 - 22

2 t^{2} - 2 t + 1

b, \frac{4 x ^{2} + b ^{2} - 2 b x}{3} = y

0 = a^{2} - 2 a + 2.34

x^{2} + (6 + 2 x)^{2} = (9 + 2 x)^{2}

144.3 x^{2} - 350.98 x + 49.9947 = 0

What are the solutions to the equation 6.5=((x+x^2+5x))/2 ?
The solutions to the equation 6.5=((x+x^2+5x))/2 are x=-3+sqrt(22),x=-3-sqrt(22)
Find the zeros of 6.5=((x+x^2+5x))/2
The zeros of 6.5=((x+x^2+5x))/2 are x=-3+sqrt(22),x=-3-sqrt(22)