What are the solutions to the equation (x-3/2)(2x-9/2)=11 ?

The solutions to the equation (x-3/2)(2x-9/2)=11 are x= 17/4 ,x=-1/2

Find the zeros of (x-3/2)(2x-9/2)=11

The zeros of (x-3/2)(2x-9/2)=11 are x= 17/4 ,x=-1/2

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(x - \frac{3}{2}) (2 x - \frac{9}{2}) = 11

x = \frac{17}{4}, x = - \frac{1}{2}

Solution steps

(x - \frac{3}{2}) (2 x - \frac{9}{2}) = 11

Expand

(x - \frac{3}{2}) (2 x - \frac{9}{2}) : 2 x^{2} - \frac{15}{2} x + \frac{27}{4}

2 x^{2} - \frac{15}{2} x + \frac{27}{4} = 11

Move

11

to the left side

- \frac{17}{4} - \frac{15}{2} x + 2 x^{2} = 0

Write in the standard form

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

2 x^{2} - \frac{15 x}{2} - \frac{17}{4} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - \frac{15}{2} ) \pm ( - \frac{15}{2} ) ^{2} - 4 \cdot 2 ( - \frac{17}{4} )}{2 \cdot 2}

(- \frac{15}{2})^{2} - 4 \cdot 2 (- \frac{17}{4}) = \frac{19}{2}

x_{1, 2} = \frac{- ( - \frac{15}{2} ) \pm \frac{19}{2}}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - \frac{15}{2} ) + \frac{19}{2}}{2 \cdot 2}, x_{2} = \frac{- ( - \frac{15}{2} ) - \frac{19}{2}}{2 \cdot 2}

x = \frac{- ( - \frac{15}{2} ) + \frac{19}{2}}{2 \cdot 2} : \frac{17}{4}

x = \frac{- ( - \frac{15}{2} ) - \frac{19}{2}}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

x = \frac{17}{4}, x = - \frac{1}{2}

∣ 2 a - 1 ∣ < 3

\frac{120 π}{180}

∣ x + 5 ∣ - 6 = 8

18 n^{3} + 39 n^{2} - 15 n

n^{2} + 4 n - 5

What are the solutions to the equation (x-3/2)(2x-9/2)=11 ?
The solutions to the equation (x-3/2)(2x-9/2)=11 are x= 17/4 ,x=-1/2
Find the zeros of (x-3/2)(2x-9/2)=11
The zeros of (x-3/2)(2x-9/2)=11 are x= 17/4 ,x=-1/2