What are the solutions to the equation 1/2 x^2+3/8 x=2 ?

The solutions to the equation 1/2 x^2+3/8 x=2 are x=(-3+sqrt(265))/8 ,x=(-3-sqrt(265))/8

Find the zeros of 1/2 x^2+3/8 x=2

The zeros of 1/2 x^2+3/8 x=2 are x=(-3+sqrt(265))/8 ,x=(-3-sqrt(265))/8

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\frac{1}{2} x^{2} + \frac{3}{8} x = 2

x = \frac{- 3 + 265}{8}, x = \frac{- 3 - 265}{8}

Decimal

x = 1.65985 \dots, x = - 2.40985 \dots

Solution steps

\frac{1}{2} x^{2} + \frac{3}{8} x = 2

Find Least Common Multiplier of

2, 8 : 8

Multiply by LCM=

8

\frac{1}{2} x^{2} \cdot 8 + \frac{3}{8} x \cdot 8 = 2 \cdot 8

Simplify

4 x^{2} + 3 x = 16

Move

16

to the left side

4 x^{2} + 3 x - 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 4 ( - 16 )}{2 \cdot 4}

3^{2} - 4 \cdot 4 (- 16) = 265

x_{1, 2} = \frac{- 3 \pm 265}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 3 + 265}{2 \cdot 4}, x_{2} = \frac{- 3 - 265}{2 \cdot 4}

x = \frac{- 3 + 265}{2 \cdot 4} : \frac{- 3 + 265}{8}

x = \frac{- 3 - 265}{2 \cdot 4} : \frac{- 3 - 265}{8}

The solutions to the quadratic equation are:

x = \frac{- 3 + 265}{8}, x = \frac{- 3 - 265}{8}

(1 - x) (11 - x) + 26 = 0

8 x^{2} + 3 = 2

x^{2} + 14 x + 6 = 0

x^{2} + x = - 5

2 t^{2} + t + 9 = 2

What are the solutions to the equation 1/2 x^2+3/8 x=2 ?
The solutions to the equation 1/2 x^2+3/8 x=2 are x=(-3+sqrt(265))/8 ,x=(-3-sqrt(265))/8
Find the zeros of 1/2 x^2+3/8 x=2
The zeros of 1/2 x^2+3/8 x=2 are x=(-3+sqrt(265))/8 ,x=(-3-sqrt(265))/8