What are the solutions to the equation 25-1/4 x-1/2 =-3/4 x^2+25 ?

The solutions to the equation 25-1/4 x-1/2 =-3/4 x^2+25 are x=-2/3 ,x=1

Find the zeros of 25-1/4 x-1/2 =-3/4 x^2+25

The zeros of 25-1/4 x-1/2 =-3/4 x^2+25 are x=-2/3 ,x=1

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25 - \frac{1}{4} x - \frac{1}{2} = - \frac{3}{4} x^{2} + 25

x = - \frac{2}{3}, x = 1

Decimal Notation

x = - 0.66666 \dots, x = 1

Solution steps

25 - \frac{1}{4} x - \frac{1}{2} = - \frac{3}{4} x^{2} + 25

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

25 \cdot 4 - \frac{1}{4} x \cdot 4 - \frac{1}{2} \cdot 4 = - \frac{3}{4} x^{2} \cdot 4 + 25 \cdot 4

Simplify

100 - x - 2 = - 3 x^{2} + 100

- x + 98 = - 3 x^{2} + 100

Switch sides

- 3 x^{2} + 100 = - x + 98

Move

98

to the left side

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

Move

x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

1^{2} - 4 (- 3) \cdot 2 = 5

x_{1, 2} = \frac{- 1 \pm 5}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 1 + 5}{2 ( - 3 )}, x_{2} = \frac{- 1 - 5}{2 ( - 3 )}

x = \frac{- 1 + 5}{2 ( - 3 )} : - \frac{2}{3}

x = \frac{- 1 - 5}{2 ( - 3 )} : 1

The solutions to the quadratic equation are:

x = - \frac{2}{3}, x = 1

8 x^{2} = 968

\frac{3 ( x + 1 )}{2} - \frac{5 ( x - 1 )}{3} = \frac{( x + 1 ) ( x + 2 )}{6}

- 2 x^{2} + 23 x - 40 = 0

6 x^{2} + 3.6 x = 0

744 - 64 x - x^{2} = 0

What are the solutions to the equation 25-1/4 x-1/2 =-3/4 x^2+25 ?
The solutions to the equation 25-1/4 x-1/2 =-3/4 x^2+25 are x=-2/3 ,x=1
Find the zeros of 25-1/4 x-1/2 =-3/4 x^2+25
The zeros of 25-1/4 x-1/2 =-3/4 x^2+25 are x=-2/3 ,x=1