What are the solutions to the equation x^2+1/2 x+1/16 = 4/9 ?

The solutions to the equation x^2+1/2 x+1/16 = 4/9 are x= 5/12 ,x=-11/12

Find the zeros of x^2+1/2 x+1/16 = 4/9

The zeros of x^2+1/2 x+1/16 = 4/9 are x= 5/12 ,x=-11/12

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x^{2} + \frac{1}{2} x + \frac{1}{16} = \frac{4}{9}

x = \frac{5}{12}, x = - \frac{11}{12}

Decimal Notation

x = 0.41666 \dots, x = - 0.91666 \dots

Solution steps

x^{2} + \frac{1}{2} x + \frac{1}{16} = \frac{4}{9}

Find Least Common Multiplier of

2, 16, 9 : 144

Multiply by LCM=

144

x^{2} \cdot 144 + \frac{1}{2} x \cdot 144 + \frac{1}{16} \cdot 144 = \frac{4}{9} \cdot 144

Simplify

144 x^{2} + 72 x + 9 = 64

Move

64

to the left side

144 x^{2} + 72 x - 55 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 72 \pm 7 2 ^{2} - 4 \cdot 144 ( - 55 )}{2 \cdot 144}

7 2^{2} - 4 \cdot 144 (- 55) = 192

x_{1, 2} = \frac{- 72 \pm 192}{2 \cdot 144}

Separate the solutions

x_{1} = \frac{- 72 + 192}{2 \cdot 144}, x_{2} = \frac{- 72 - 192}{2 \cdot 144}

x = \frac{- 72 + 192}{2 \cdot 144} : \frac{5}{12}

x = \frac{- 72 - 192}{2 \cdot 144} : - \frac{11}{12}

The solutions to the quadratic equation are:

x = \frac{5}{12}, x = - \frac{11}{12}

12 x^{2} - 15 x + 4 = 0

x^{2} + 2.8 x = 23.04

(9 + 2 x) (4 + 2 x) = 84

x^{2} + 5 x - 4

(x + 2) (x + 4) = 2 x

What are the solutions to the equation x^2+1/2 x+1/16 = 4/9 ?
The solutions to the equation x^2+1/2 x+1/16 = 4/9 are x= 5/12 ,x=-11/12
Find the zeros of x^2+1/2 x+1/16 = 4/9
The zeros of x^2+1/2 x+1/16 = 4/9 are x= 5/12 ,x=-11/12