What are the solutions to the equation ((18-x)^2)/2 =((18-x)*18)/2*1/3 ?

The solutions to the equation ((18-x)^2)/2 =((18-x)*18)/2*1/3 are x=18,x=12

Find the zeros of ((18-x)^2)/2 =((18-x)*18)/2*1/3

The zeros of ((18-x)^2)/2 =((18-x)*18)/2*1/3 are x=18,x=12

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\frac{( 18 - x ) ^{2}}{2} = \frac{( 18 - x ) \cdot 18}{2} \cdot \frac{1}{3}

x = 18, x = 12

Solution steps

\frac{( 18 - x ) ^{2}}{2} = \frac{( 18 - x ) \cdot 18}{2} \cdot \frac{1}{3}

Simplify

2 \cdot 3 : 6

\frac{( 18 - x ) ^{2}}{2} = \frac{( 18 - x ) \cdot 18 \cdot 1}{6}

Find Least Common Multiplier of

2, 6 : 6

Multiply by LCM=

6

\frac{( 18 - x ) ^{2}}{2} \cdot 6 = \frac{( 18 - x ) \cdot 18 \cdot 1}{6} \cdot 6

Simplify

3 (- x + 18)^{2} = 18 (18 - x)

Expand

3 (- x + 18)^{2} : 3 x^{2} - 108 x + 972

Expand

18 (18 - x) : 324 - 18 x

3 x^{2} - 108 x + 972 = 324 - 18 x

Move

18 x

to the left side

3 x^{2} - 90 x + 972 = 324

Move

324

to the left side

3 x^{2} - 90 x + 648 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 90 ) \pm ( - 90 ) ^{2} - 4 \cdot 3 \cdot 648}{2 \cdot 3}

(- 90)^{2} - 4 \cdot 3 \cdot 648 = 18

x_{1, 2} = \frac{- ( - 90 ) \pm 18}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 90 ) + 18}{2 \cdot 3}, x_{2} = \frac{- ( - 90 ) - 18}{2 \cdot 3}

x = \frac{- ( - 90 ) + 18}{2 \cdot 3} : 18

x = \frac{- ( - 90 ) - 18}{2 \cdot 3} : 12

The solutions to the quadratic equation are:

x = 18, x = 12

∣ 5 a + 4 ∣ = ∣ 6 a - 8 ∣

4 x^{2} = 5 - 2 x

∣ x - 3 ∣ < 5

16 x - 35 = 7 x - 8

6 - \frac{3}{4} x > 9

What are the solutions to the equation ((18-x)^2)/2 =((18-x)*18)/2*1/3 ?
The solutions to the equation ((18-x)^2)/2 =((18-x)*18)/2*1/3 are x=18,x=12
Find the zeros of ((18-x)^2)/2 =((18-x)*18)/2*1/3
The zeros of ((18-x)^2)/2 =((18-x)*18)/2*1/3 are x=18,x=12